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22Nd British Combinatorial Conference University of St 22nd British Combinatorial Conference University of St Andrews 5th – 10th July 2009 Monday 6th July Time Theatre A Theatre B Theatre C Theatre D Room 314 Room 204 09:00 – 09:30 Welcome & registration 09:30 – 10:30 Cameron (p. 6) — — — — — 10:30 – 11:00 Coffee 11:00 – 11:20 Alderson (p. 7) Kisielewicz (p. 7) Yamashita (p. 7) Tsikouras (p. 8) Poghosyan (p. 8) — 11:25 – 11:45 FIRE!! FIRE!! FIRE!! FIRE!! FIRE!! — 11:50 – 12:10 FIRE!! FIRE!! FIRE!! FIRE!! FIRE!! — 12:15 – 12:35 FIRE!! FIRE!! FIRE!! FIRE!! FIRE!! — 12:40 – 14:00 Lunch 14:00 – 15:00 Noy (p. 9) — — — — — 15:05 – 15:25 Kochol (p. 10) Bailey (Rob.) (p. 10) Burger (p. 10) Abreu (p. 11) Lin (p. 11) 15:30 – 15:50 Kayibi (p. 12) Balof (p. 12) Chang (p. 12) Blackburn (p. 13) Lo (p. 13) — 15:55 – 16:20 Tea 16:20 – 16:40 Ivanov (p. 14) Lopez (p. 15) Drapal (p. 15) Tsuchiya (p. 16) Whitty (p. 16) — 16:45 – 17:05 Ivanov (p. 14) Miralles (p. 17) Egan (p. 17) Mitjana (p. 18) Suarez (p. 18) — 17:10 – 17:30 Ivanov (p. 14) Montagh (p. 19) Ellingham (p. 19) Montejano (p. 20) Wu (p. 20) — 17:35 – 17:55 Smith (p. 21) Arumugam (p. 21) de Bruyn (p. 21) Lichiardopol (p. 22) — 2 Tuesday 7th July Time Theatre A Theatre B Theatre C Theatre D Room 314 Room 204 09:30 – 10:30 Riordan (p. 23) — — — — — 10:30 – 11:00 Coffee 11:00 – 11:20 Santos (p. 24) Dalfo (p. 24) Falcone (p. 24) Ceballos (p. 25) Mukae (p. 25) — 11:25 – 11:45 Huang (p. 26) Caceres (p. 26) Forbes (p. 26) Valenzuela (p. 27) Mukwembi (p. 27) — 11:50 – 12:10 Korpelainen (p. 28) Casselgren (p. 28) Gonzalez-Moreno (p. 28) Junosza-Szaniawski (p. 29) Mycroft (p. 29) — 12:15 – 12:35 Brignall (p. 30) Chiang (p. 30) Marcote (p. 30) The Business Meeting Mynhardt (p. 31) — 12:40 – 13:00 Bailey (Ros.) (p. 32) Akbari (p. 32) Labbate (p. 32) The Business Meeting Auger (p. 33) — 13:00 – 14:00 Lunch 14:00 – 15:00 Khosrovshahi (p. 34) — — — — — 15:05 – 15:25 de Beule (p. 35) Nagy (p. 35) Grannell (p. 35) Keedwell (p. 36) Cooley (p. 36) — 15:30 – 15:50 Gacs (p. 37) Encinas (p. 37) Wang (p. 37) Moori (p. 38) Noble (p. 38) — 15:55 – 16:20 Tea 16:20 – 16:40 Carmona (p. 39) Dankelmann (p. 39) Bau (p. 39) Morgan (p. 40) Sapir (p. 40) — 16:45 – 17:05 Hirschfeld (p. 41) Danziger (p. 41) Ohman (p. 41) Egawa (p. 42) Shinohara (p. 42) — 17:10 – 17:30 Panario (p. 43) Osthus (p. 43) O’Neill (p. 43) Siemons (p. 44) Patkos (p. 44) — 17:35 – 17:55 Vega (p. 45) Penman (p. 45) Stones (p. 45) Suzuki (p. 46) Eisermann (p. 46) — 18:00 – 18:20 Merola (p. 47) Ando (p. 47) Brunat (p. 47) Levit (p. 48) Gillespie (p. 48) — Wednesday 8th July Time Theatre A Theatre B Theatre C Theatre D Room 314 Room 204 09:30 – 10:30 Royle (p. 49) — — — — — 10:30 – 11:00 Coffee 11:00 – 11:20 Vilches (p. 50) Ferguson (p. 50) Soicher (p. 50) Kempner (p. 51) Przykucki (p. 51) Hallez (p. 51) 11:25 – 11:45 Csikvari (p. 52) Pirzada (p. 52) Patterson (p. 52) Pike (p. 53) Firoozabadi (p. 53) Canale (p. 53) 11:50 – 12:10 Plummer (p. 54) Gago (p. 54) Webb (p. 54) Dentice (p. 55) Sulkowska (p. 55) Newman (p. 55) 12:15 – 12:35 Hilton (p. 56) Fujita (p. 56) Ushio (p. 56) Cvetkovic (p. 57) Villar (p. 57) Sanayei (p. 57) 3 Thursday 9th July Time Theatre A Theatre B Theatre C Theatre D Room 314 Room 204 09:30 – 10:30 Bonisoli (p. 23) — — — — — 10:30 – 11:00 Coffee 11:00 – 11:20 De Clerck (p. 59) Garcia-Vazquez (p. 59) Britz (p. 59) Umar (p. 60) Ghanbari (p. 60) Heger (p. 60) 11:25 – 11:45 Vanhove (p. 61) Puertas (p. 61) Christian (p. 61) Wanless (p. 62) Aalipour (p. 62) Burgess (p. 62) 11:50 – 12:10 Foniok (p. 63) Goldberg (p. 63) Hall (p. 63) Waters (p. 64) Salas (p. 64) Olsen (p. 64) 12:15 – 12:35 Sokal (p. 65) Manlove (p. 65) Fountoulakis (p. 65) Yamada (p. 66) Roy (p. 66) Guevara (p. 66) 12:40 – 14:00 Lunch 14:00 – 15:00 Kuhn¨ (p. 67) — — — — — 15:05 – 15:25 Cavenagh (p. 68) Schmitt (p. 68) Ghosh (p. 68) Georgiou (p. 69) Haddad (p. 69) Camara (p. 69) 15:30 – 15:50 Sapozhenko (p. 70) Henning (p. 70) Cariolaro (p. 70) Yeo (p. 71) Phillips (p. 71) Mani (p. 71) 15:55 – 16:20 Tea 16:20 – 16:40 Nakamoto (p. 72) Grech (p. 72) Simanihuruk (p. 72) Vaughan (p. 73) Jones (p. 73) Hetherington (p. 73) 16:45 – 17:05 Siran (p. 74) Holroyd (p. 74) Rutherford (p. 74) Jorgensen (p. 75) Tsuchiya (p. 75) Papalamprou (p. 75) 17:10 – 17:30 Swart (p. 76) Moffatt (p. 76) Haggkvist (p. 76) Tong (p. 77) Jimenez (p. 77) Ozeki (p. 77) 17:35 – 17:55 Rowlinson (p. 78) Kuchta (p. 78) Schauz (p. 78) Kay (p. 79) Treglown (p. 79) Ali (p. 79) 4 Friday 10th July Time Theatre A Theatre B Theatre C Theatre D Room 314 Room 204 09:30 – 10:30 Kostochka (p. 80) — — — — — 10:30 – 11:00 Coffee 11:00 – 11:20 Meierling (p. 81) Jerrum (p. 81) Walczak (p. 81) Moura (p. 82) Andren (p. 82) 11:25 – 11:45 Griggs (p. 83) McLeod (p. 83) Ariannejad (p. 83) Konstantinova (p. 84) Ashrafi (p. 84) 11:50 – 12:10 Shen (p. 85) Allen (p. 85) Yu (p. 85) vanVuuren (p. 86) Bhatti (p. 86) 12:15 – 12:35 Preece (p. 87) Kardos (p. 87) Rattan (p. 87) Blinovsky (p. 88) Hoffmann-Ostenhof (p. 88) — 12:40 – 14:00 Lunch 14:00 – 15:00 Haemers (p. 89) — — — — — 15:05 – 15:30 Tea 15:30 – 16:30 Problem Session — — — — — 5 Monday 6th of July, 9:30 – 10:30 Theatre A Optimal block designs for combinatorialists Peter Cameron (Queen Mary, University of London, UK) To a combinatorialist, a design is usually a 2-design or balanced incomplete-block design. However, 2-designs do not necessarily exist in all cases where a statistician might wish to use one to design an experiment. As a result, statisticians need to consider structures much more general than the combinatorialist’s designs, and to decide which one is “best” in a given situation. This leads to the theory of optimal designs. There are several concepts of optimality, and no general consensus about which one to use in any particular situation. For block designs with fixed block size k, all these optimality criteria are determined by a graph, the concurrence graph of the design, and more specifically, by the eigenvalues of the Laplacian matrix of the graph. It turns out that the optimality criteria most used by statisticians correspond to properties of this graph which are interesting in other contexts: D-optimality involves maximizing the number of spanning trees; A-optimality involves minimizing the sum of resistances between all pairs of terminals (when the graph is re- garded as an electrical circuit, with each edge being a one-ohm resistor); and E-optimality involves maximizing the smallest eigenvalue of the Laplacian (the corresponding graphs are likely to have good expansion and random walk properties). If you are familiar with these properties, you may expect that related “nice” properties such as regularity and large girth (or even symmetry) may tend to hold; some of our examples may come as a surprise! The aim of this talk is to point out that the optimal design point of view unifies various topics in graph theory and design theory, and suggests some interesting open problems to which combinatorialists of all kinds might turn their expertise. We describe in some detail both the statistical background and the mathematics of various topics such as Laplace eigenvalues of graphs. 6 Monday 6th of July, 11:00 – 11:20 Theatre A Theatre B Theatre C Spreads, arcs, and multiple wavelength codes Totally Symmetric Colored Graphs A degree sum condition with connectivity for Tim Alderson Andrzej Kisielewicz relative length of longest paths and cycles University of New Brunswick Saint John University of Wrocław, Poland Tomoki Yamashita [email protected] [email protected] Kitasato University Coauthors: K. E. Mellinger Coauthors: Mariusz Grech [email protected] We present several new families of constant weight, We describe almost all edge-colored complete graphs For a graph G, p(G) and c(G) denote the orders of multiple wavelength (2-dimensional) optical orthogo- that are fully symmetric with respect to colors a longest path and a longest cycle of G, respectively. nal codes (2D-OOCs) with ideal auto-correlation λa = and transitive on every set of edges of the same A connected graph G is hamiltonian if and only if 0, and with cross correlations λ = 1, 2. We also color. This generalizes the recent description of self- p(G) − c(G) = 0, and any longest cycle of a graph provide a construction which yields multiple weight complementary symmetric graphs by Peisert and gives G is dominating if p(G) − c(G) ≤ 1. A cycle C of a codes. All families presented are either optimal with examples of permutation groups that require more than graph G is said to be a dominating cycle if V (G \ C) respect to the Johnson bound (J-optimal) or are asymp- 5 colors to be represented as the automorphism group is an independent set.
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