Publications of N.C. Wormald

[1] N. Wormald. Non-existence of certain supplementary difference sets. Bull. Austral. Math. Soc., 13, 343–348, 1975.

[2] L.S. Sterling and N. Wormald. A remark on the construction of designs for two-way elimination of heterogeneity. Bull. Austral. Math. Soc., 14, 383–388, 1976.

[3] F. Harary, R.W. Robinson, and N. Wormald. The divisibility theorem for isomorphic factorisations of complete graphs. J. Graph Theory, 1, 187–188, 1977.

[4] N. Wormald. Counting labelled 3-connected graphs. J. Graph Theory, 1, 383–384, 1977.

[5] P. Eades, J.S. Wallis, and N. Wormald. A note on asymptotic existence results for orthogonal designs. In Combinatorial Mathematics V, volume 522 of Springer Lectures Notes in Mathematics, pages 76–90, 1977.

[6] N. Wormald. Achiral plane trees. J. Graph Theory, 2, 189–208, 1978.

[7] F. Harary, R.W. Robinson, and N.C. Wormald. Isomorphic factorisations I: Com- plete graphs. Trans. Amer. Math. Soc., 242, 243–260, 1978.

[8] N.C. Wormald. Triangles in labelled cubic graphs. In Combinatorial Mathematics, volume 686 of Springer Lecture Notes in Mathematics, pages 337–343, 1978.

[9] F. Harary, R.W. Robinson, and N.C. Wormald. Isomorphic factorisations III: Com- plete multipartite graphs. In Combinatorial Mathematics, volume 686 of Springer Lecture Notes in Mathematics, pages 47–54, 1978.

[10] F. Harary, R.W. Robinson, and N.C. Wormald. Isomorphic factorisations V: Di- rected graphs. Mathematika, 25, 279–285, 1978.

[11] N. Wormald and E.M. Wright. The exponential generating fuction of labelled blocks. Discrete Math., 25, 93–96, 1979.

[12] N. Wormald. Enumeration of labelled graphs I: 3-connected graphs. J. London Math. Soc. (2), 19, 7–12, 1979.

[13] N.C. Wormald. Enumeration of labelled graphs II: Cubic graphs with a given con- nectivity. J. London Math. Soc. (2), 20, 1–7, 1979.

[14] N. Wormald. A 4-chromatic graph with a special plane drawing. J. Austral. Math.Soc. (series A), 28, 1–8, 1979.

[15] N. Wormald. On the number of automorphisms of a regular graph. Proc. Amer. Math. Soc., 76, 345–348, 1979. [16] N.C. Wormald. Classifying k-connected cubic graphs. In Combinatorial Mathematics VI, volume 748 of Springer Lecture Notes in Mathematics, pages 199–206, 1979.

[17] R.C. Read and N.C. Wormald. The number of labelled 4-regular graphs. J. Graph Theory, 4, 203–212, 1980.

[18] N.C. Wormald. A correspondence for rooted planar maps. Ars Combinatoria, 9, 11–28, 1980.

[19] N.C. Wormald. On the number of planar maps. Canad. J. Math., 33, 1–11, 1981.

[20] R.C. Read and N.C. Wormald. Counting the ten-point graphs by partition. J. Graph Theory, 5, 183–196, 1981.

[21] N.C. Wormald. The asymptotic connectivity of labelled regular graphs. J. Combi- natorial Theory (Series B), 31, 156–167, 1981.

[22] N.C. Wormald. The asymptotic distribution of short cycles in random regular graphs. J. Combinatorial Theory (Series B), 31, 168–182, 1981.

[23] N.C. Wormald. Counting unrooted planar maps. Discrete Math., 36, 205–225, 1981.

[24] N.C. Wormald. The number of labelled cubic graphs with no triangles. Congressus Numerantium, 33, 359–378, 1981.

[25] L.B. Richmond and N.C. Wormald. The asymptotic number of convex polyhedra. Trans. Amer. Math. Soc., 273, 721–735, 1982.

[26] N.C. Wormald. Subtrees of large tournaments. In Combinatorial Mathematics X, volume 1036 of Springer Lecture Notes in Mathematics, pages 417–419, 1983.

[27] R.W. Robinson and N.C. Wormald. Numbers of cubic graphs. J. Graph Theory, 7, 463–467, 1983.

[28] L.H. Clark and N.C. Wormald. Hamilton-like indices of graphs. Ars Combinatoria, 15, 131–148, 1983.

[29] N.J. Pullman and N.C. Wormald. Regular graphs with prescribed odd girth. Utilitas Math., 24, 243–251, 1983.

[30] N.C. Wormald. Isomorphic factorizations VII. Regular graphs and tournaments. J. Graph Theory, 8, 117–122, 1984.

[31] A.J. Guttmann and N.C. Wormald. On the number of spiral self-avoiding walks. J. Phys. A: Math. Gen., 17, L271–L274, 1984. (Corrigendum: J. Phys. A: Math. Gen. 17 (1984) p.3614).

[32] N.C. Wormald. Generating random regular graphs. J. Algorithms, 5, 247–280, 1984.

[33] G. Chartrand, F. Saba, and N.C. Wormald. Bridge and cycle degrees of vertices of graphs. Internat. J. Math. & Math. Sci., 7, 351–360, 1984. [34] R.W. Robinson and N.C. Wormald. Existence of long cycles in random cubic graphs. In D.M. Jackson and S.A. Vanstone, editors, Enumeration and Design, pages 251– 270. Academic Press (Toronto), 1984.

[35] B.D. McKay and N.C. Wormald. Automorphisms of random graphs with specified degrees. Combinatorica, 4, 325–338, 1984.

[36] E.A. Bender, L.B. Richmond, and N.C. Wormald. Almost all chordal graphs split. J. Austral. Math. Soc. (Series A), 38, 214–221, 1985.

[37] K.B. Reid and N.C. Wormald. Embedding oriented n-trees in tournaments. Studia Sci. Math. Hungar., 18, 377–387, 1983.

[38] B. Bollob´as,A. Saito, and N.C. Wormald. Regular factors of regular graphs. J. Graph Theory, 9, 97–103, 1985.

[39] N.C. Wormald. Counting labelled chordal graphs. Graphs and Combinatorics, 1, 193–200, 1985.

[40] C.E. Praeger, P. Schultz, and N.C. Wormald. Enumeration of rooted trees with a height distribution. Ars Combinatoria, 19A, 191–204, 1985.

[41] E.A. Bender and N.C. Wormald. The number of loopless planar maps. Discrete Math., 54, 235–237, 1985.

[42] R.D. Cameron, C.J. Colbourn, R.C. Read, and N.C. Wormald. Cataloguing the graphs on 10 vertices. J. Graph Theory, 9, 551–562, 1985.

[43] N.C. Wormald. Enumeration of cyclically 4-connected cubic graphs. J. Graph The- ory, 9, 563–573, 1985.

[44] E.A. Bender and N.C. Wormald. Almost all convex polyhedra are asymmetric. Canad. J. Math., 27, 854–871, 1985.

[45] L.B. Richmond, R.W. Robinson, and N.C. Wormald. On hamilton cycles in 3- connected cubic maps. In B. Alspach and C.D. Godsil, editors, Cycles in Graphs, volume 27 of Annals of Discrete Mathematics, pages 141–150. North-Holland, 1985.

[46] E.A. Bender, L.B. Richmond, R.W. Robinson, and N.C. Wormald. The asymptotic number of acyclic digraphs I. Combinatorica, 6, 15–22, 1986.

[47] N.C. Wormald. A simpler proof of the asymptotic formula for the number of unla- belled r-regular graphs. Indian J. Math., 28, 43–47, 1986.

[48] P.D. Eades, B.D. McKay, and N.C. Wormald. On an edge crossing problem. In Proc. Ninth Aust. Comp. Sci. Conf., pages 327–334, Australian National University, 1986.

[49] N.C. Wormald. On the frequency of 3-connected subgraphs of planar graphs. Bull. Austral. Math. Soc., 34, 309–317, 1986. [50] D. de Caen, P. Erd˝os,N.J. Pullman, and N.C. Wormald. Extremal clique coverings of complementary graphs. Combinatorica, 6, 309–314, 1986.

[51] L.A. Sz´ekely and N.C. Wormald. Generating functions for the Frobenius Problem with 2 and 3 generators. Mathematical Chronicle, 15, 49–57, 1986.

[52] R.E. Canfield and N.C. Wormald. M´enagenumbers, bijections, and P -recursiveness. Discrete Math., 63, 117–129, 1987.

[53] E.A. Bender, C.E. Praeger, and N.C. Wormald. Optimal worst-case trees. Acta Informatica, 24, 475–489, 1987.

[54] N.C. Wormald. Generating random unlabelled graphs. SIAM J. Comput., 16, 717– 727, 1987.

[55] M.N. Ellingham and N.C. Wormald. Isomorphic factorization of regular graphs and 3-regular multigraphs. J. London Math. Soc. (2), 37, 14–24, 1988.

[56] L.B. Richmond and N.C. Wormald. Random triangulations of the plane. Europ. J. Combinatorics, 9, 61–71, 1988.

[57] E.A. Bender and N.C. Wormald. The number of rooted convex polyhedra. Canad. Math. Bull., 31, 99–102, 1988.

[58] E.A. Bender and N.C. Wormald. Random trees in random graphs. Proc. Amer. Math. Soc., 103, 314–320, 1988.

[59] P.D. Eades and N.C. Wormald. Performance guarantees for a plotter optimisation heuristic. INFOR, 25, 314–319, 1987.

[60] N.C. Wormald. The asymptotic number of nonsingular and nonseparable maps on the projective plane. Ars Combinatoria, 23B, 133–137, 1987.

[61] E.A. Bender and N.C. Wormald. The asymptotic number of rooted nonseparable maps on a surface. J. Combinatorial Theory (Series A), 49, 370–380, 1988.

[62] L.A. Sz´ekely and N.C. Wormald. Bounds on the measurable chromatic number of Rn. Discrete Mathematics, 75, 343–372, 1989.

[63] B. Jackson and N.C. Wormald. Cycles containing matchings and pairwise compatible euler tours. J. Graph Theory, 14, 127–138, 1990.

[64] B.D. McKay and N.C. Wormald. Uniform generation of random regular graphs of moderate degree. J. Algorithms, 11, 52–67, 1990.

[65] M. Carter, M. Hendy, D. Penny, L.A. Sz´ekely, and N.C. Wormald. On the distribu- tion of lengths of evolutionary trees. SIAM J. Discrete Math., 3, 38–47, 1990.

[66] L.B. Richmond and N.C. Wormald. Almost all quadrangular dissections of the disc are asymmetrical. Math. Chronicle, 19, 63–71, 1990. [67] P.D. Eades and N.C. Wormald. Fixed edge-length graph drawing is NP-hard. Dis- crete Applied Mathematics, 28, 111–134, 1990.

[68] L. Bolian, B.D. McKay, Zhang Ke Min, and N.C. Wormald. The exponent set of symmetric primitive (0,1)-matrices with zero trace. Linear Algebra and Applications, 133, 121–131, 1990.

[69] D.A. Holton, B. Jackson, A. Saito, and N.C. Wormald. Removable edges in 3- connected graphs. J. Graph Theory, 14, 465–473, 1990.

[70] B.D. McKay and N.C. Wormald. Asymptotic enumeration by degree sequence of graphs of high degree. Europ. J. Combinatorics, 11, 565–580, 1990.

[71] B. Jackson and N.C. Wormald. k-walks in graphs. Australasian J. Combinatorics, 2, 135–146, 1990.

[72] B.D. McKay and N.C. Wormald. Asymptotic enumeration by degree sequence of graphs with degrees o(n1/2). Combinatorica, 11, 369–382, 1991.

[73] B. Jackson and N.C. Wormald. Longest cycles in 3-connected planar graphs. J. Combinatorial Theory (Series B), 54, 291–321, 1992.

[74] R.W. Robinson and N.C. Wormald. Almost all cubic graphs are hamiltonian. Ran- dom Structures and Algorithms, 3, 117–125, 1992.

[75] A.M. Moffat, O. Petersson, and N.C. Wormald. Further analysis of an adaptive sort- ing algorithm. In Proceedings of the 15’th Australian Computer Science Conference, pages 603–613, University of Tasmania, 1992.

[76] B. Jackson and N.C. Wormald. Longest cycles in 3-connected graphs of bounded maximum degree. In Rolf Rees, editor, Graphs, Matrices and Designs, volume 139 of Lecture Notes in Pure and Applied Mathematics, pages 237–254. Dekker, New York, 1992.

[77] I.G. Enting, A.J. Guttmann, L.B. Richmond, and N.C. Wormald. Enumeration of almost convex polygons on the square lattice. Random Structures and Algorithms, 3, 445–461, 1992.

[78] A.M. Moffat, O. Petersson, and N.C. Wormald. Sorting and/by merging finger trees. In T. Ibaraki et al., editor, Proc. International Symposium on Algorithms and Computation, LNCS, pages 499–508, Nagoya, Japan, 1992. Springer Verlag.

[79] A. Ruci´nskiand N.C. Wormald. Random graph processes with degree restrictions. Combinatorics, Probability and Computing, 1, 169–180, 1992.

[80] B.D. McKay and N.C. Wormald. Uniform generation of random latin rectangles. J. Combinatorial Mathematics and Combinatorial Computing, 9, 179–186, 1991.

[81] P.D. Eades, X. Lin, and N.C. Wormald. Performance guarantees for motion planning with temporal uncertainty. Aust. Computer Journal, 25, 21–29, 1993. [82] E.A. Bender, L.B. Richmond, and N.C. Wormald. Submaps of maps IV: Degree restricted nonplanar maps. Ars Combinatoria, 35A, 135–142, 1993.

[83] P.J. Cameron, C.E. Praeger, and N.C. Wormald. Infinite highly arc transitive di- graphs and universal covering digraphs. Combinatorica, 14, 377–396, 1993.

[84] R.W. Robinson and N.C. Wormald. Almost all regular graphs are hamiltonian. Random Structures and Algorithms, 5, 363–374, 1994.

[85] Z. Gao and N.C. Wormald. Spanning eulerian subgraphs of bounded degree in triangulations. Graphs and Combinatorics, 10, 123–131, 1994.

[86] P. Eades and N.C. Wormald. Edge crossings in drawings of bipartite graphs. Algo- rithmica, 11, 379–403, 1994.

[87] G. Havas, B.S. Majewski, N.C. Wormald, and Z.J. Czech. Graphs, hypergraphs and hashing. In 19th International Workshop on Graph-Theoretic Concepts in Computer Science (WG’93), volume 790 of Lecture Notes in Computer Science, pages 153–165, Berlin, 1994. (Utrecht, 1993), Springer Verlag.

[88] L.B. Richmond and N.C. Wormald. Almost all maps are asymmetric. J. Combina- torial Theory (Series B), 63, 1–7, 1995.

[89] B. Jackson and N.C. Wormald. Long cycles and 3-connected spanning subgraphs of bounded degree in 3-connected K1,d-free graphs. J. Combinatorial Theory (Series B), 63, 163–169, 1995.

[90] E.A. Bender, L.B. Richmond, and N.C. Wormald. Largest 4-connected components of 3-connected planar triangulations. Random Structures and Algorithms, 7, 273– 285, 1995.

[91] N.C. Wormald. Differential equations for random processes and random graphs. Annals of Applied Probability, 5, 1217–1235, 1995.

[92] E.A. Bender, Z. Gao, L.B. Richmond, and N.C. Wormald. Asymptotic properties of rooted 3-connected maps on surfaces. J. Austral. Math. Soc. (Series A), 60, 31–41, 1996.

[93] B. Pittel, J. Spencer, and N. Wormald. Sudden emergence of a giant k-core in a random graph. J. Combinatorial Theory, Series B, 67, 111–151, 1996.

[94] M. Brazil, T. Cole, J.H. Rubinstein, D.A. Thomas, J.F. Weng, and N.C. Wormald. Minimal steiner trees for 2k × 2k checkerboards. J. Combinatorial Theory, Series A, 73, 91–110, 1996.

[95] A. Frieze, M. Jerrum, M. Molloy, R.W. Robinson, and N.C. Wormald. Generating and counting hamilton cycles in random regular graphs. Journal of Algorithms, 21, 176–198, 1996.

[96] N.C. Wormald. The perturbation method for triangle-free random graphs. Random Structures and Algorithms, 9, 253–270, 1996. [97] M.P. Ng and N.C. Wormald. Reconstruction of rooted trees from subtrees. Discrete Applied Mathematics, 69, 19–31, 1996.

[98] B.S. Majewski, N.C. Wormald, G. Havas, and Z.J. Czech. A family of perfect hashing methods. Computer Journal, 39, 547–554, 1996.

[99] B. Jackson and N.C. Wormald. On the linear k-arboricity of cubic graphs. Discrete Mathematics, 162, 293–297, 1996.

[100] R.E.L. Aldred, B.D. McKay, and N.C. Wormald. Small hypohamiltonian graphs. J. Combinatorial Mathematics and Combinatorial Computing, 23, 143–152, 1997.

[101] M. Molloy, H. Robalewska, R.W. Robinson, and N.C. Wormald. 1-factorisations of random regular graphs. Random Structures and Algorithms, 10, 305–321, 1997.

[102] J.H. Rubinstein, D.A. Thomas, and N.C. Wormald. Steiner trees for terminals constrained to curves. SIAM J. Discrete Math., 10, 1–17, 1997.

[103] B.D. McKay and N.C. Wormald. The degree sequence of a random graph. I. The models. Random Structures and Algorithms, 11, 97–117, 1997.

[104] M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F. Weng, and N.C. Wormald. Full minimal steiner trees on lattice sets. J. Combinatorial Theory, Series A, 78, 51–91, 1997.

[105] M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F. Weng, and N.C. Wormald. Minimal steiner trees for rectangular arrays of lattice points. J. Combinatorial Theory, Series A, 79, 181–208, 1997.

[106] A. Ruci´nskiand N.C. Wormald. Random graph processes with maximum degree 2. Annals of Applied Probability, 7, 183–199, 1997.

[107] D. Stark and N.C. Wormald. The asymptotic number of d-dimensional convex poly- gons. J. Combinatorial Theory, Series A, 80, 196–217, 1997.

[108] M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F. Weng, and N.C. Wormald. Short- est networks on spheres. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 40, 453–461, 1998.

[109] T. Lindquester and N.C. Wormald. Factorisation of regular graphs into forests of paths. Discrete Mathematics, 186, 217–226, 1998.

[110] R.E.L. Aldred and N.C. Wormald. Linear k-arboricity of regular graphs. Aus- tralasian Journal of Combinatorics, 18, 97–104, 1998.

[111] A. Moffat, O. Petersson, and N.C. Wormald. A tree-based mergesort. Acta Infor- matica, 35, 775–793, 1998.

[112] W.D. Smith and N.C. Wormald. Geometric separator theorems and applications. In 39th Annual Symposium on Foundations of Computer Science – FOCS ’98, pages 232–243, Palo Alto, CA, 1998. [113] A. Knopfmacher, A. Odlyzko, B. Pittel, L.B. Richmond, D. Stark, G. Szekeres, and N.C. Wormald. On set partitions with unequal block sizes. Electronic Journal of Combinatorics, 6, Research Paper 2, 36 pp., 1999.

[114] N.C. Wormald. Models of random regular graphs. In J.D. Lamb and D.A. Preece, editors, Surveys in Combinatorics, 1999, volume 267 of London Mathematical Society Lecture Note Series, pages 239–298. Cambridge University Press, Cambridge, 1999.

[115] N.C. Wormald. The differential equation method for random graph processes and greedy algorithms. In M. Karo´nskiand H.J. Pr¨omel,editors, Lectures on Approxi- mation and Randomized Algorithms, pages 73–155. PWN, Warsaw, 1999.

[116] Z. Gao and N.C. Wormald. The size of the largest components in random planar maps. SIAM J. Discrete Math., 12, 217–228, 1999.

[117] A. Steger and N.C. Wormald. Generating random regular graphs quickly. Combi- natorics, Probability and Computing, 8, 377–396, 1999.

[118] W. Duckworth, N.C. Wormald, and M. Zito. Approximation algorithms for find- ing sparse 2-spanners of 4-connected planar triangulations. In R.J. Simpson and R. Raman, editors, Proc. Tenth Australasian Workshop on Combinatorial Algo- rithms, pages 63–75, Perth, Western Australia, 1999. Curtin University.

[119] A. Telcs and N.C. Wormald. Branching and tree indexed random walks on fractals. J. Applied Probab., 36, 999–1011, 1999.

[120] M. Ng, M. Steel, and N.C. Wormald. The difficulty of constructing a leaf-labelled tree including or avoiding given subtrees. Discrete Applied Mathematics, 98, 227– 235, 2000.

[121] Z. Gao and N.C. Wormald. The distribution of the maximum vertex degree in random planar maps. J. Combinatorial Theory, Series A, 89, 201–230, 2000.

[122] H.D. Robalewska and N.C. Wormald. Random star processes. Combinatorics, Prob- ability and Computing, 9, 33–43, 2000.

[123] H. Assiyatun and N.C. Wormald. Covering regular graphs with forests of small trees. Australasian Journal of Combinatorics, 22, 219–226, 2000.

[124] M. Brazil, D. Lee, J.H. Rubinstein, D.A. Thomas, J.F. Weng, and N.C. Wormald. Network optimisation of underground mine designs. Proc. Australasian Inst. of Mining and Metallurgy, 305, 57–65, 2000.

[125] J.H. Kim and N.C. Wormald. Random matchings which induce Hamilton cycles, and hamiltonian decompositions of random regular graphs. J. Combinatorial Theory, Series B, 81, 20–44, 2001.

[126] I.M. Wanless and N.C. Wormald. Regular graphs with no homomorphisms onto cycles. J. Combinatorial Theory, Series B, 82, 155–160, 2001. [127] R.W. Robinson and N.C. Wormald. Hamilton cycles containing randomly selected edges in random cubic graphs. Random Structures and Algorithms, 19, 128–147, 2001.

[128] J.H. Rubinstein, D.A. Thomas, and N.C. Wormald. A polynomial algorithm for a constrained traveling salesman problem. Networks, 38, 68–75, 2001.

[129] Z. Gao, I.M. Wanless, and N.C. Wormald. Counting 5-connected planar triangula- tions. J. Graph Theory, 38, 18–35, 2001.

[130] M. Krivelevich, B. Sudakov, V. Vu, and N.C. Wormald. Random regular graphs of high degree. Random Structures and Algorithms, 18, 346–363, 2001.

[131] N. Alon, V.J. Teague, and N.C. Wormald. Linear arboricity and linear k-arboricity of regular graphs. Graphs and Combinatorics, 17, 11–16, 2001.

[132] M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F. Weng, and N.C. Wormald. Gradient- constrained minimum networks I: Fundamentals. J. Global Optim., 21, 139–155, 2001.

[133] A. Ruci´nskiand N.C. Wormald. Connectedness of graphs generated by a random d-process. J. Austral. Math. Soc., 72, 67–85, 2002.

[134] C.S. Greenhill, S. Janson, J. H. Kim, and N.C. Wormald. Permutation pseudographs and contiguity. Combinatorics, Probability and Computing, 11, 273–298, 2002.

[135] W. Duckworth and N.C. Wormald. Minimum independent dominating sets of ran- dom cubic graphs. Random Structures and Algorithms, 21, 147–161, 2002.

[136] B.D. McKay, I.M. Wanless, and N.C. Wormald. Asymptotic enumeration of graphs with a given upper bound on the maximum degree. Combinatorics, Probability and Computing, 11, 373–392, 2002.

[137] W. Duckworth, N.C. Wormald, and M. Zito. Maximum induced matchings of ran- dom cubic graphs. Journal of Computational and Applied Mathematics, 142, 39–50, 2002.

[138] J. D´ıaz,N. Do, M. Serna, and N.C. Wormald. Bounds on the max and min bisection of random cubic and random 4-regular graphs. In J. Rolim and S. Vadhan, editors, Randomization and Approximation Techniques in Computer Science, volume 2483 of Lecture Notes in Computer Science, pages 114–125. Springer, 2002.

[139] M. Brazil, D. Lee, J.H. Rubinstein, D.A. Thomas, J.F. Weng, and N.C. Wormald. A network model to optimise cost in underground mine design. Trans. South African Inst. of Electrical Engineers, 93, 97–103, 2002.

[140] S. Bau, N.C. Wormald, and S.M. Zhou. Decycling numbers of random regular graphs. Random Structures and Algorithms, 21, 397–413, 2002.

[141] E.A. Bender, Z. Gao, and N.C. Wormald. The number of labeled 2-connected planar graphs. Electronic Journal of Combinatorics, 9, Research Paper 43, 13 pp., 2002. [142] Z. Gao and N.C. Wormald. Enumeration of rooted cubic planar maps. Annals of Combinatorics, 6, 313–325, 2002.

[143] W. Duckworth, N.C. Wormald, and M. Zito. A PTAS for a sparsest 2-spanner of a 4-connected planar triangulation. Journal of Discrete Algorithms, 1, 67–76, 2003.

[144] M. Krivelevich, B. Sudakov, V. Vu, and N.C. Wormald. On the probability of independent sets in random graphs. Random Structures and Algorithms, 22, 1–14, 2003.

[145] B. Pittel and N.C. Wormald. Asymptotic enumeration of sparse graphs with a minimum degree constraint. J. Combinatorial Theory, Series A, 101, 249–263, 2003.

[146] N.C. Wormald. Analysis of greedy algorithms on graphs with bounded degrees, Eurocomb ’01 (Barcelona). Discrete Mathematics, 273, 235–260, 2003.

[147] C.S. Greenhill, A. Ruci´nski, and N.C. Wormald. Connectedness of the degree bounded star process. Combinatorics, Probability and Computing, 12, 269–283, 2003.

[148] Z. Gao and N.C. Wormald. Sharp concentration of the number of submaps in random planar triangulations. Combinatorica, 23, 467–486, 2003.

[149] R. Castelo and N.C. Wormald. Enumeration of P4-free chordal graphs. Graphs and Combinatorics, 19, 467–474, 2003.

[150] M. Brazil, D.H. Lee, M. Van Leuven, J.H. Rubinstein, D.A. Thomas, and N.C. Wormald. Optimising declines in underground mines. Mining Technology, 112, 164– 170, 2003.

[151] J. D´ıaz,N. Do, M. Serna, and N.C. Wormald. Bounds on the max and min bisection of random cubic and random 4-regular graphs. Theoretical Computer Science, 307, 531–547, 2003.

[152] N.C. Wormald. Random graphs and asymptotics. In J.L. Gross and J. Yellen, editors, Handbook of Graph Theory, chapter 8.2, pages 817–836. CRC, Boca Raton, 2004.

[153] C.S. Greenhill, A. Ruci´nski,and N.C. Wormald. Random hypergraph processes with degree restrictions. Graphs and Combinatorics, 20, 319–332, 2004.

[154] C.S. Greenhill, J.H. Kim, and N.C. Wormald. Hamiltonian decompositions of ran- dom bipartite regular graphs. Journal of Combinatorial Theory, Series B, 90, 195– 222, 2004.

[155] B.D. McKay, N.C. Wormald, and B. Wysocka. Short cycles in random regular graphs. Electronic Journal of Combinatorics, 11(1), Research Paper 66, 12 pp., 2004.

[156] Z. Gao and N.C. Wormald. Asymptotic normality determined by high moments, and submap counts of random maps. Probability Theory and Related Fields, 130, 368–376, 2004. [157] J. D´ıaz, M. Serna, and N.C. Wormald. Computation of the bisection width for random d-regular graphs. In LATIN 2004: Theoretical informatics, volume 2976 of Lecture Notes in Computer Science, pages 49–58. Springer, Berlin, 2004.

[158] T. Bohman, A. Frieze, and N.C. Wormald. Avoidance of a giant component in half the edge set of a random graph. Random Structures and Algorithms, 25, 432–449, 2004.

[159] B. Pittel and N.C. Wormald. Counting connected graphs inside-out. J. Combinato- rial Theory, Series B, 93, 127–172, 2005. (Corrigendum: J. Combinatorial Theory, Series B, 98, 835–837, 2008).

[160] J. Neˇsetˇriland N.C. Wormald. The acyclic edge chromatic number of a random d-regular graph is d + 1. J. Graph Theory, 49, 69–74, 2005.

[161] A. Frieze and N.C. Wormald. Random k-sat: A tight threshold for moderately growing k. Combinatorica, 25, 297–305, 2005.

[162] J. D´ıaz,X. Perez, M. Serna, and N.C. Wormald. Connectivity for wireless agents moving on a cycle or grid. In STACS 2005, Lecture Notes in Computer Science, 3404, pages 353–364. Springer, Berlin, 2005.

[163] M. Brazil, D. Lee, J. H. Rubinstein, D. A. Thomas, J. F. Weng, and N. C. Wormald. Optimisation in the design of underground mine access. In R. Dimitrakopoulos, editor, Orebody Modelling and Strategic Mine Planning, Spectrum Series 14, pages 121–124. AusIMM, 2005. (Second edition, 2007, pp. 141–144).

[164] W. Duckworth and N.C. Wormald. On the independent domination number of random regular graphs. Combinatorics, Probability and Computing, 15, 513–522, 2006.

[165] J.H. Rubinstein, J.F. Weng, and N. Wormald. Approximations and lower bounds for the length of minimal euclidean steiner trees. J. Global Optimization, 35, 573–592, 2006.

[166] S. Gerke, C. Greenhill, and N. Wormald. The generalised acyclic edge chromatic number of random regular graphs. J. Graph Theory, 53, 101–125, 2006.

[167] J. Cain and N. Wormald. Encores on cores. Electronic Journal of Combinatorics, 13, Research Paper 81, 13 pp., 2006.

[168] H. Assiyatun and N. Wormald. 3-star factors in random regular graphs. Europ. J. Combinatorics, 27, 1249–1262, 2006.

[169] D.A. Thomas, M. Brazil, D. Lee, and N.C. Wormald. Network modelling of under- ground mine layout: Two case studies. International Transactions in Operational Research, 14, 143–158, 2007.

[170] L. Shi and N. Wormald. Colouring random 4-regular graphs. Combinatorics, Prob- ability and Computing, 16, 309–344, 2007. [171] L. Shi and N. Wormald. Colouring random regular graphs. Combinatorics, Proba- bility and Computing, 16, 459–494, 2007.

[172] J. D´ıaz,M. Serna, and N.C. Wormald. Bounds on the bisection width for random d-regular graphs. Theoretical Computer Science, 382, 120–130, 2007.

[173] J. Lauer and N. Wormald. Large independent sets in regular graphs of large girth. J. Combinatorial Theory, Series B, 97, 999–1009, 2007.

[174] S. Janson and N. Wormald. Rainbow hamilton cycles in random regular graphs. Random Structures and Algorithms, 30, 35–49, 2007.

[175] A. Telcs, N.C. Wormald, and S.M. Zhou. Hamiltonicity of random graphs produced by 2-processes. Random Structures and Algorithms, 31, 450 – 481, 2007.

[176] J. Cain, P. Sanders, and N. Wormald. The random graph threshold for k- orientiability and a fast algorithm for optimal multiple-choice allocation. In Pro- ceedings of 18th Annual ACM-SIAM SODA, pages 469–476, 2007.

[177] P. Pralat M.-E. Messinger, R.J. Nowakowski and N. Wormald. Cleaning random d-regular graphs with brushes using a degree-greedy algorithm. In CAAN 2007, volume 4852 of Lecture Notes in Computer Science, pages 13–26, 2007.

[178] J. Spencer and N. Wormald. Birth control for giants. Combinatorica, 27, 587–628, 2007.

[179] M. Brazil, P.A. Grossman, D.H. Lee, J.H. Rubinstein, D.A. Thomas, and N.C. Wormald. Constrained path optimisation for underground mine layout. In The 2007 International Conference of Applied and Engineering Mathematics (ICAEM07), London, pages 856–861, 2007. This is the conference version of “Decline design in underground mines using constrained path optimisation” listed below.

[180] N.C. Wormald and S. Zhou. Large forbidden trade volumes of random graphs. Discrete Mathematics, 308, 2751–2755, 2008.

[181] Z. Gao and N.C. Wormald. Distribution of subgraphs of random regular graphs. Random Structures and Algorithms, 32, 38–48, 2008.

[182] C.S. Greenhill, F.B. Holt, and N. Wormald. Expansion properties of a random regular graph after random vertex deletions. Europ. J. Combin., 29, 1139–1150, 2008.

[183] J. D´ıaz,X. Perez, M. Serna, and N.C. Wormald. Walkers on the cycle and the grid. SIAM J. Discrete Math., 22, 747–775, 2008.

[184] C. Hoppen and N. Wormald. Induced forests in regular graphs with large girth. Combinatorics, Probability and Computing, 17, 389–410, 2008.

[185] M. Brazil, P.A. Grossman, D.H. Lee, J.H. Rubinstein, D.A. Thomas, and N.C. Wormald. Decline design in underground mines using constrained path optimisation. Mining Technology: IMM Transactions Section A, 117, 93–99, 2008. [186] N. Alon, P. Pralat,and N. Wormald. Cleaning d-regular graphs with brushes. SIAM J. Discrete Math., 23, 233–250, 2008.

[187] P. Gao and N. Wormald. Short cycle distribution in random regular graphs produced by pegging. Random Structures and Algorithms, 34, 54–86, 2009.

[188] P. Pralatand N. Wormald. Growing protean graphs. Internet Mathematics, 4, 1–16, 2009.

[189] P. Gao and N. Wormald. Rate of convergence of the short cycle distribution in random regular graphs generated by pegging. Electronic Journal of Combinatorics, 16, RP 44, 19 pp., 2009.

[190] Z. Gao, V.A. Liskovets, and N. Wormald. Enumeration of unrooted odd-valent regular planar maps. Annals of Combinatorics, 13, 233–259, 2009.

[191] J. D´ıaz,A.C. Kaporis, G.D. Kemkes, L.M. Kirousis, X. P´erez,and N. Wormald. On the chromatic number of random 5-regular graphs. J. Graph Theory, 61, 157–191, 2009.

[192] E. Mossel, D. Weitz, and N. Wormald. On the hardness of sampling independent sets beyond the tree threshold. Probability Theory and Related Fields, 143, 401–439, 2009.

[193] M. Brazil, P.A. Grossman, D. Lee, J.H. Rubinstein, D.A. Thomas, and N.C. Wormald. Access optimisation tools in underground mine design. In International Symposium. Orebody Modelling and Strategic Mine Planning: Old and New Dimen- sions in a Changing World. Proceedings of the Orebody Modelling and Strategic Mine Planning Conference 16–17 March 2009, pages 237–241. Australasian Institute of Mining and Metallurgy, 2009.

[194] W. Richards and N. Wormald. Representing small group evolution. In Proceedings - 12th IEEE International Conference on Computational Science and Engineering, CSE 2009 (SocialCom 2009, Vancouver, August 2009), volume 4, pages 159–165, 2009.

[195] E.A. Bender, A.B. Olde Daalhuis, Z. Gao, L.B. Richmond, and N.C. Wormald. Asymptotics of some convolutional recurrences. Electronic Journal of Combina- torics, 17, Research Paper 1, 11 pp., 2010.

[196] N. Alon and N. Wormald. High degree graphs contain large-star factors. In A. Schri- jver Gy. Katona and T. Szonyi, editors, Fete of Combinatorics and Computer Sci- ence, volume 20 of Bolyai Soc. Math. Studies, pages 9–21. Springer, 2010.

[197] G. Kemkes, X. P´erez-Gim´enez,and N. Wormald. On the chromatic number of random d-regular graphs. Advances in Mathematics, 223, 300–328, 2010.

[198] P. Gao and N. Wormald. Load balancing and orientability thresholds for random hypergraphs. In Proceedings of STOC, pages 97–104. (ACM), 2010. (The journal version of this paper is called ‘Orientability thresholds for random hypergraphs’). [199] O. Riordan and N. Wormald. The diameter of sparse random graphs. Combinatorics, Probability and Computing, 19, 835–926, 2010.

[200] W. Duckworth and N. Wormald. Linear programming and the worst-case analysis of greedy algorithms on cubic graphs. Electronic Journal of Combinatorics, 17, Research Paper 177, 29 pp., 2010.

[201] I. Benjamini, C. Hoppen, E. Ofek, P. Pralat,and N. Wormald. Geodesics and almost geodesic cycles in random regular graphs. J. Graph Theory, 66, 115–136, 2011.

[202] M. Krivelevich, B. Sudakov, and N. Wormald. Regular induced subgraphs of a random graph. Random Structures and Algorithms, 38, 235–250, 2011.

[203] S. Gerke, A. Steger, and N. Wormald. Pegging graphs yields a small diameter. Combinatorics, Probability and Computing, 20, 239–248, 2011.

[204] T. M¨uller,X. P´erez-Gim´enez,and N. Wormald. Disjoint hamilton cycles in the random geometric graph. J. Graph Theory, 68, 299–322, 2011.

[205] P. Pralat,J. Verstra¨ete,and N. Wormald. On the threshold for k-regular subgraphs of random graphs. Combinatorica, 31, 565–581, 2011.

[206] P. Gao, Y. Su, and N. Wormald. Induced subgraphs in sparse random graphs with given degree sequence. European Journal of Combinatorics, 33, 1142–1166, 2012.

[207] M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F. Weng, and N. Wormald. Gradient- constrained minimum networks, III. fixed topology. Journal of Optimization Theory and Applications, 155, 336–354, 2012.

[208] F.C. Botelho, N. Wormald, and N. Ziviani. Cores of random r-partite hypergraphs. Information Processing Letters, 112, 314–319, 2012.

[209] G. Kemkes and N. Wormald. An improved upper bound on the length of the longest cycle of a post-critical random graph. SIAM J. Discrete Math., 27, 342–362, 2013.

[210] A. Mehrabian and N. Wormald. On the stretch factor of randomly embedded random graphs. Discrete and Computational Geometry, 49, 647–658, 2013.

[211] X. P´erez-Gim´enezand N. Wormald. Asymptotic enumeration of strongly connected digraphs by vertices and edges. Random Structures and Algorithms, 43, 80–114, 2013.

[212] E. Ebrahimzadeh, L. Farczadi, P. Gao, A. Mehrabian, C.M. Sato, N. Wormald, and J. Zung. On the longest paths and the diameter in random apollonian networks (extended abstract). Electronic Notes in Discrete Mathematics, 43, 355–365, 2013.

[213] G. Kemkes, C.M. Sato, and N. Wormald. Asymptotic enumeration of sparse 2- connected graphs. Random Structures and Algorithms, 43, 354–376, 2013.

[214] B. Kolesnik and N. Wormald. Lower bounds for the isoperimetric numbers of random regular graphs. SIAM J. Discrete Math., 28, 553–575, 2014. [215] I. Benjamini, G. Kozma, and N. Wormald. The mixing time of the giant component of a random graph. Random Structures & Algorithms, 45, 383–407, 2014.

[216] W. Richards and N. Wormald. The evolution and structure of social networks. Network Science, 2, 326–340, 2014.

[217] E. Ebrahimzadeh, L. Farczadi, P. Gao, A. Mehrabian, C.M. Sato, N. Wormald, and J. Zung. On the longest paths and the diameter in random apollonian networks. Random Structures & Algorithms, 45, 703–725, 2014.

[218] A. Mehrabian and N. Wormald. It’s a small world for random surfers. In Approx- imation, randomization, and combinatorial optimization 2014 (extended abstract), pages 857–871, 2014.

[219] P. Gao and N. Wormald. Orientability thresholds for random hypergraphs. Combi- natorics, Probability and Computing, 24, 774–824, 2015.

[220] P. Gao and N. Wormald. Uniform generation of random regular graphs. In Proceed- ings of 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pages 1218–1230, 2015.

[221] H. Acan, A. Collevecchio, A. Mehrabian, and N. Wormald. On the push&pull protocol for rumour spreading. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (extended abstract), pages 405–412, 2015.

[222] P. Gao and N. Wormald. Enumeration of graphs with a heavy-tailed degree sequence. Advances in Mathematics, 287, 412–450, 2016.

[223] P. Pralatand N. Wormald. Meyniel’s conjecture holds for random graphs. Random Structures & Algorithms, 48, 396–421, 2016.

[224] C. Hoppen and N. Wormald. Properties of regular graphs with large girth via local algorithms. J. Combinatorial Theory, Series B, 121, 367–397, 2016.

[225] A. Collevecchio, A. Mehrabian, and N. Wormald. Longest paths in random apollo- nian networks and largest r-ary subtrees of random d-ary recursive trees. Journal of Applied Probability, 53, 846–856, 2016.

[226] A. Mehrabian and N. Wormald. It’s a small world for random surfers. Algorithmica, 76, 344–380, 2016.

[227] E. Lubetzky, J. Kahn, and N. Wormald. The threshold for combs in random graphs. Random Structures & Algorithms, 48, 794–802, 2016.

[228] E. Lubetzky, J. Kahn, and N. Wormald. Cycle factors and renewal theory. Commu- nications in Pure and Applied Mathematics, 70, 289–339, 2017.

[229] H. Acan, A. Collevecchio, A. Mehrabian, and N. Wormald. On the push&pull protocol for rumour spreading. SIAM J. Discrete Math., 31, 647–668, 2017.

[230] L. Kang and N. Wormald. Minimum power dominating sets of random cubic graphs. J Graph Theory, 85, 152–171, 2017. [231] C. Hoppen and N. Wormald. Local algorithms, regular graphs of large girth, and random regular graphs. Combinatorica (accepted for publication).

[232] P. Gao and N. Wormald. Uniform generation of random regular graphs. SIAM J. Computing (accepted for publication).

[233] P. Pralatand N. Wormald. Almost all 5-regular graphs have a 3-flow. (submitted).

[234] P. Pralat and N. Wormald. Meyniel’s conjecture holds for random regular graphs. (submitted).

[235] A. Coja-Oghlan and N. Wormald. The number of satisfying assignments of random regular k-sat formulas. (submitted).

[236] D. Stark and N.C. Wormald. The probability of nonexistence of a subgraph in a moderately sparse random graph. (submitted).

[237] P. Gao and N. Wormald. Uniform generation of random graphs with power-law degree sequences. (submitted).