36 DM14 Abstracts

Total Page:16

File Type:pdf, Size:1020Kb

36 DM14 Abstracts 36 DM14 Abstracts IP0 University of Oxford Hot Topic Session: The Existence of Designs [email protected] We prove the existence conjecture for combinatorial de- signs, answering a question of Steiner from 1853. More IP4 generally, we show that the natural divisibility conditions Submodular Functions and Their Applications are sufficient for clique decompositions of simplicial com- plexes that satisfy a certain pseudorandomness condition. Submodular functions, a discrete analogue of convex func- tions, have played a fundamental role in combinatorial op- timization since the 1970s. In the last decade, there has Peter Keevash been renewed interest in submodular functions due to their University of Oxford role in algorithmic game theory, as well as numerous appli- [email protected] cations in machine learning. These developments have led to new questions as well as new algorithmic techniques. I will discuss the concept of submodularity, its unifying role IP1 in combinatorial optimization, and a few illustrative appli- The Graph Regularity Method cations. I will describe some recent algorithmic advances, in particular the concept of multilinear relaxation, and the Szemerdi’s regularity lemma is one of the most powerful role of symmetry in proving hardness results for submod- tools in graph theory, with many applications in combina- ular optimization. I will conclude by discussing possible torics, number theory, discrete geometry, and theoretical extensions of the notion of submodularity, and some fu- computer science. Roughly speaking, it says that every ture challenges. large graph can be partitioned into a small number of parts such that the bipartite subgraph between almost all pairs Jan Vondrak of parts is random-like. Several variants of the regularity IBM Almaden Research Center lemma have since been established with many further ap- [email protected] plications. I will discuss recent progress in understanding the quantitative aspects of these lemmas and their appli- cations. IP5 Approximation Algorithms Via Matrix Covers Jacob Fox MIT I will describe a general technique for obtaining approx- [email protected] imate solutions of hard quadratic optimization problems using economical covers of high dimensional sets by small cubes. The analysis of the method leads to intriguing al- IP2 gorithmic, combinatorial, geometric, extremal and proba- Rota’s Conjecture bilistic questions. Based on joint papers with Troy Lee, Adi Shraibman and Santosh Vempala. In 1970, Gian-Carlo Rota posed a conjecture giving a suc- cinct combinatorial characterization of the linear depen- Noga Alon dencies among a finite set of vectors in a vector space over Tel-Aviv University any given finite field. I will discuss the conjecture as well [email protected] as joint work with Bert Gerards and Geoff Whittle that led to a solution. IP6 Jim Geelen Interlacing Families and Kadison–Singer University of Waterloo [email protected] This talk will focus on the resolution of two conjectures that have been shown to be equivalent to open problems in a number of fields, most famously a problem due to Kadi- IP3 son and Singer concerning the foundations of mathematical Covering Systems of Congruences physics. This will include introducing a new technique for establishing the existence of certain combinatorial objects A distinct covering system of congruences is a collection that we call the ”method of interlacing polynomials.” The ai mod mi,1<m1 <m2 < ... < mk, whose union is the technique seems to be interesting in its own right (it was integers. Covering systems were introduced by Paul Erdos, also the main tool for resolving the existence of Ramanujan who used the system graphs of arbitrary degree). This represents join work with Z =(0mod2)∪(0 mod 3)∪(1 mod 4)∪(3 mod 8)∪(7 mod 12)∪Dan(23 Spielmanmod 24) of Yale University and Nikhil Srivastava of Microsoft Research, India. to produce an odd arithmetic progression none of whose members is of the form a prime plus a power of two. Two Adam Marcus well-known questions of Erdos concern covering systems. Yale University The minimum modulus problem asks if there exist distinct [email protected] covering systems for which m1 is arbitrarily large. The odd modulus problem asks for a distinct covering system with all moduli odd. I will describe aspects of my negative an- IP7 swer to the minimum modulus problem and ongoing joint Hamilton Decompositions of Graphs and Digraphs work with Pace Nielsen toward the odd modulus problem. The arguments involve techniques from graph theory and In this talk I will survey recent results on Hamilton decom- PDE. positions, i.e. decompositions of the edge-set of a graph or digraph into edge-disjoint Hamilton cycles. One example Robert Hough is a conjecture of Kelly from 1968, which states that every DM14 Abstracts 37 regular tournament has a Hamilton decomposition. We Jozsef Balogh prove this conjecture for large tournaments. In fact, we University of Illinois prove a far more general result, which has further appli- [email protected] cations. Another example is the Hamilton decomposition conjecture, which was posed by Nash-Williams in 1970. It states that every regular graph on n vertices with mini- CP1 mum degree at least n/2 has a Hamilton decomposition Percolation in the Weighted Random Connection (joint work with Bela Csaba, Allan Lo, Deryk Osthus and Model Andrew Treglown). We propose the weighted random connection model, with Daniela Kuhn the goal to predict and better understand the spread of in- University of Birmingham fectious diseases. Each individual of a population is charac- [email protected] terized by two parameters: its position and risk behavior, where the probability of transmissions among individuals increases in the individual risk factors, and decays in their IP8 Euclidean distance. Our main result is on the almost sure The Complexity of Graph and Hypergraph Expan- existence of an infinite component in the weighed random sion Problems connection model, which corresponds to the outbreak of an infectious disease. We use results on the random connec- The expansion of a graph is a fundamental parameter with tion model and site percolation in Z2. many connections in mathematics and applications in com- puter science. Two basic variants of expansion are edge- Milan Bradonjic expansion (minimum ratio of the number of edges leav- Mathematics of Networks and Communications ing a subset of vertices to the total number of edge inci- Bell Labs, Alcatel-Lucent dent to the subset) and vertex expansion (minimum ratio [email protected] of number of vertices adjacent to a subset to the size of the subset). Both are NP-hard to compute exactly and CP1 the current√ best polynomial-time algorithms provide ei- ther an O( log n)OPT√ solution these problems, or, for Degeneracy in R-Mat Generated Graphs edge-expansion, an O( OPT ) solution. The latter is via Cheeger’s inequality relating edge expansion to the second The degeneracy of a graph G is the minimum possible value smallest eigenvalue of the graph Laplacian, and provides of d such that every subgraph of G has a vertex with de- an efficient method to check if a graph is an edge expander gree at most d. It is known that the degeneracy of an (i.e., has edge expansion is at least some constant). In this Erd˝os-R´enyi random graph is bounded with high probabil- talk, we survey recent developments on the following lines: ity. We examine degeneracy in the popular recursive ma- 1. What is the analog of expansion for partitioning a graph trix (R-MAT) random graph model, of which Erd˝os-R´enyi into multiple parts (more than 2), and how does Cheeger’s is a special case, and determine whether its asymptotic inequality generalize? 2. Is there a Cheeger-type inequal- behavior parallels that of Erd˝os-R´enyi graphs. ity for vertex expansion? How to efficiently verify whether Alex Chin a graph is a vertex expander? 3. Do there exist algorithms North Carolina State University with better performance? 4. How do these parameters, [email protected] inequalities and algorithms extend to hypergraphs? Santosh Vempala Timothy Goodrich Georgia Institute of Technology Valparaiso University [email protected] [email protected] Blair Sullivan SP1 North Carolina State University 2014 Dnes Knig Prize Lecture-The number of Ks,t- [email protected] free graphs The problem of enumerating H-free graphs with a given CP1 number of vertices has been studied for almost forty years. Identifying Codes and Searching with Balls in As a result, a great deal is known about this problem. Graphs When H is not bipartite, we have not only good estimates of the number of H-free graphs, but also fairly precise We address the following search theory problem: what is structural characterisation of a typical such graph. On the the minimum number of queries that is needed to deter- contrary, not much is known in case when H is bipartite. mine an unknown vertex in a graph G if queries are balls A few years ago, we proved asymptotically optimal upper with respect to the graph distance and the answer to a bounds on the number of graphs not containing a fixed query is YES if the unknown vertex lies in the ball and complete bipartite graph Ks,t. This was the first infinite NO otherwise. We study adaptive or non-adaptive versions family of bipartite graphs for which such a bound was es- of this problem for the following classes of graphs: hyper- tablished. Since then, the method developed in our proof cubes, the Erd˝os-R´enyi random graph model and graphs has found several interesting applications to a large class of bounded maximum degree. of related problems.
Recommended publications
  • An Algorithm for Drawing Planar Graphs
    An Algorithm for Drawing Planar Graphs Bor Plestenjak IMFMTCS University of Ljubljana Jadranska SI Ljubljana Slovenia email b orplestenjakfmfuniljsi AN ALGORITHM FOR DRAWING PLANAR GRAPHS SUMMARY A simple algorithm for drawing connected planar graphs is presented It is derived from the Fruchterman and Reingold spring emb edding algorithm by deleting all repulsive forces and xing vertices of an outer face The algorithm is implemented in the system for manipulating discrete mathematical structures Vega Some examples of derived gures are given Key words Planar graph drawing Forcedirected placement INTRODUCTION A graph G is planar if and only if it is p ossible to draw it in a plane without any edge intersections Every connected planar graph admits a convex drawing ie a planar drawing where every face is drawn as a convex p olygon We present a simple and ecient algorithm for convex drawing of a connected planar graph In addition to a graph most existing algorithms for planar drawing need as an input all the faces of a graph while our algorithm needs only one face of a graph to draw it planarly Let G b e a connected planar graph with a set of vertices V fv v g and a set of edges E 1 n fu v u v g Let W fw w w g V b e an ordered list of vertices of an arbitrary face in 1 1 m m 1 2 k graph G which is chosen for the outer face in the drawing The basic idea is as follows We consider graph G as a mechanical mo del by replacing its vertices with metal rings and its edges with elastic bands of zero length Vertices of the
    [Show full text]
  • Triple Connected Line Domination Number for Some Standard and Special Graphs
    International Journal of Advanced Scientific Research and Management, Volume 3 Issue 8, Aug 2018 www.ijasrm.com ISSN 2455-6378 Triple Connected Line Domination Number For Some Standard And Special Graphs A.Robina Tony1, Dr. A.Punitha Tharani2 1 Research Scholar (Register Number: 12519), Department of Mathematics, St.Mary’s College(Autonomous), Thoothukudi – 628 001, Tamil Nadu, India, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli – 627 012, Tamil Nadu, India 2 Associate Professor, Department of Mathematics, St.Mary’s College(Autonomous), Thoothukudi – 628 001, Tamil Nadu, India, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012, Tamil Nadu, India Abstract vertex domination, the concept of edge The concept of triple connected graphs with real life domination was introduced by Mitchell and application was introduced by considering the Hedetniemi. A set F of edges in a graph G is existence of a path containing any three vertices of a called an edge dominating set if every edge in E graph G. A subset S of V of a non - trivial graph G is – F is adjacent to at least one edge in F. The said to be a triple connected dominating set, if S is a dominating set and the induced subgraph <S> is edge domination number γ '(G) of G is the triple connected. The minimum cardinality taken minimum cardinality of an edge dominating set over all triple connected dominating set is called the of G. An edge dominating set F of a graph G is triple connected domination number and is denoted a connected edge dominating set if the edge by γtc(G).
    [Show full text]
  • Coloring Problems in Graph Theory Kacy Messerschmidt Iowa State University
    Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2018 Coloring problems in graph theory Kacy Messerschmidt Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Mathematics Commons Recommended Citation Messerschmidt, Kacy, "Coloring problems in graph theory" (2018). Graduate Theses and Dissertations. 16639. https://lib.dr.iastate.edu/etd/16639 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Coloring problems in graph theory by Kacy Messerschmidt A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Mathematics Program of Study Committee: Bernard Lidick´y,Major Professor Steve Butler Ryan Martin James Rossmanith Michael Young The student author, whose presentation of the scholarship herein was approved by the program of study committee, is solely responsible for the content of this dissertation. The Graduate College will ensure this dissertation is globally accessible and will not permit alterations after a degree is conferred. Iowa State University Ames, Iowa 2018 Copyright c Kacy Messerschmidt, 2018. All rights reserved. TABLE OF CONTENTS LIST OF FIGURES iv ACKNOWLEDGEMENTS vi ABSTRACT vii 1. INTRODUCTION1 2. DEFINITIONS3 2.1 Basics . .3 2.2 Graph theory . .3 2.3 Graph coloring . .5 2.3.1 Packing coloring . .6 2.3.2 Improper coloring .
    [Show full text]
  • Minimal K-Connected Non-Hamiltonian Graphs
    Graphs and Combinatorics (2018) 34:289–312 https://doi.org/10.1007/s00373-018-1874-z Minimal k-Connected Non-Hamiltonian Graphs Guoli Ding1 · Emily Marshall2 Received: 24 April 2017 / Revised: 31 January 2018 / Published online: 14 February 2018 © Springer Japan KK, part of Springer Nature 2018 Abstract In this paper, we explore minimal k-connected non-Hamiltonian graphs. Graphs are said to be minimal in the context of some containment relation; we focus on subgraphs, induced subgraphs, minors, and induced minors. When k = 2, we discuss all minimal 2-connected non-Hamiltonian graphs for each of these four rela- tions. When k = 3, we conjecture a set of minimal non-Hamiltonian graphs for the minor relation and we prove one case of this conjecture. In particular, we prove all 3-connected planar triangulations which do not contain the Herschel graph as a minor are Hamiltonian. Keywords Hamilton cycles · Graph minors 1 Introduction Hamilton cycles in graphs are cycles which visit every vertex of the graph. Determining their existence in a graph is an NP-complete problem and as such, there is a large body of research proving necessary and sufficient conditions. In this paper, we analyze non-Hamiltonian graphs. In particular, we consider the following general question: The first author was supported in part by NSF Grant DMS-1500699. The work for this paper was largely done while the second author was at Louisiana State University. B Emily Marshall [email protected] Guoli Ding [email protected] 1 Mathematics Department, Louisiana State University, Baton Rouge, LA 70803, USA 2 Computer Science and Mathematics Department, Arcadia University, Glenside, PA 19038, USA 123 290 Graphs and Combinatorics (2018) 34:289–312 what are the minimal k-connected non-Hamiltonian graphs? A graph is minimal if it does not contain a smaller graph with the same properties.
    [Show full text]
  • Three Topics in Online List Coloring∗
    Three Topics in Online List Coloring∗ James Carraher†, Sarah Loeb‡, Thomas Mahoney‡, Gregory J. Puleo‡, Mu-Tsun Tsai‡, Douglas B. West§‡ February 15, 2013 Abstract In online list coloring (introduced by Zhu and by Schauz in 2009), on each round the set of vertices having a particular color in their lists is revealed, and the coloring algorithm chooses an independent subset to receive that color. The paint number of a graph G is the least k such that there is an algorithm to produce a successful coloring with no vertex being shown more than k times; it is at least the choice number. We study paintability of joins with complete or empty graphs, obtaining a partial result toward the paint analogue of Ohba’s Conjecture. We also determine upper and lower bounds on the paint number of complete bipartite graphs and characterize 3-paint- critical graphs. 1 Introduction The list version of graph coloring, introduced by Vizing [18] and Erd˝os–Rubin–Taylor [2], has now been studied in hundreds of papers. Instead of having the same colors available at each vertex, each vertex v has a set L(v) (called its list) of available colors. An L-coloring is a proper coloring f such that f(v) L(v) for each vertex v. A graph G is k-choosable if an ∈ L-coloring exists whenever L(v) k for all v V (G). The choosability or choice number | | ≥ ∈ χℓ(G) is the least k such that G is k-choosable. Since the lists at vertices could be identical, always χ(G) χ (G).
    [Show full text]
  • A Survey of Graph Coloring - Its Types, Methods and Applications
    FOUNDATIONS OF COMPUTING AND DECISION SCIENCES Vol. 37 (2012) No. 3 DOI: 10.2478/v10209-011-0012-y A SURVEY OF GRAPH COLORING - ITS TYPES, METHODS AND APPLICATIONS Piotr FORMANOWICZ1;2, Krzysztof TANA1 Abstract. Graph coloring is one of the best known, popular and extensively researched subject in the eld of graph theory, having many applications and con- jectures, which are still open and studied by various mathematicians and computer scientists along the world. In this paper we present a survey of graph coloring as an important subeld of graph theory, describing various methods of the coloring, and a list of problems and conjectures associated with them. Lastly, we turn our attention to cubic graphs, a class of graphs, which has been found to be very interesting to study and color. A brief review of graph coloring methods (in Polish) was given by Kubale in [32] and a more detailed one in a book by the same author. We extend this review and explore the eld of graph coloring further, describing various results obtained by other authors and show some interesting applications of this eld of graph theory. Keywords: graph coloring, vertex coloring, edge coloring, complexity, algorithms 1 Introduction Graph coloring is one of the most important, well-known and studied subelds of graph theory. An evidence of this can be found in various papers and books, in which the coloring is studied, and the problems and conjectures associated with this eld of research are being described and solved. Good examples of such works are [27] and [28]. In the following sections of this paper, we describe a brief history of graph coloring and give a tour through types of coloring, problems and conjectures associated with them, and applications.
    [Show full text]
  • Program of the Sessions San Diego, California, January 9–12, 2013
    Program of the Sessions San Diego, California, January 9–12, 2013 AMS Short Course on Random Matrices, Part Monday, January 7 I MAA Short Course on Conceptual Climate Models, Part I 9:00 AM –3:45PM Room 4, Upper Level, San Diego Convention Center 8:30 AM –5:30PM Room 5B, Upper Level, San Diego Convention Center Organizer: Van Vu,YaleUniversity Organizers: Esther Widiasih,University of Arizona 8:00AM Registration outside Room 5A, SDCC Mary Lou Zeeman,Bowdoin upper level. College 9:00AM Random Matrices: The Universality James Walsh, Oberlin (5) phenomenon for Wigner ensemble. College Preliminary report. 7:30AM Registration outside Room 5A, SDCC Terence Tao, University of California Los upper level. Angles 8:30AM Zero-dimensional energy balance models. 10:45AM Universality of random matrices and (1) Hans Kaper, Georgetown University (6) Dyson Brownian Motion. Preliminary 10:30AM Hands-on Session: Dynamics of energy report. (2) balance models, I. Laszlo Erdos, LMU, Munich Anna Barry*, Institute for Math and Its Applications, and Samantha 2:30PM Free probability and Random matrices. Oestreicher*, University of Minnesota (7) Preliminary report. Alice Guionnet, Massachusetts Institute 2:00PM One-dimensional energy balance models. of Technology (3) Hans Kaper, Georgetown University 4:00PM Hands-on Session: Dynamics of energy NSF-EHR Grant Proposal Writing Workshop (4) balance models, II. Anna Barry*, Institute for Math and Its Applications, and Samantha 3:00 PM –6:00PM Marina Ballroom Oestreicher*, University of Minnesota F, 3rd Floor, Marriott The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 34, Issue 1 of Abstracts is ten minutes.
    [Show full text]
  • Russian Regional Report (Vol. 9, No. 1, 3 February 2004)
    Russian Regional Report (Vol. 9, No. 1, 3 February 2004) A bi-weekly publication jointly produced by the Center for Security Studies at the Swiss Federal Institute of Technology (ETH) Zurich (http://www.isn.ethz.ch) and the Transnational Crime and Corruption Center (TraCCC) at American University, Washington, DC (http://www.American.edu/traccc) TABLE OF CONTENTS TraCCC Yaroslavl Conference Crime Groups Increasing Ties to Authorities Gubernatorial Elections Sakhalin Elects New Governor Center-Periphery Relations Tyumen Oblast, Okrugs Resume Conflict Electoral Violations Khabarovsk Court Jails Election Worker Procurator Files Criminal Cases in Kalmykiya Elections Advertisements Russia: All 89 Regions Trade and Investment Guide Dynamics of Russian Politics: Putin's Reform of Federal-Regional Relations ***RRR on-line (with archives) - http://www.isn.ethz.ch/researchpub/publihouse/rrr/ TRACCC YAROSLAVL CONFERENCE CRIME GROUPS INCREASING TIES TO AUTHORITIES. Crime groups are increasingly working with public officials in Russia at the regional, and local levels, making it difficult for those seeking to enact and enforce laws combating organized crime, according to many of the criminologists who participated in a conference addressing organized crime hosted by Yaroslavl State University and sponsored by TraCCC, with support from the US Department of Justice on 20-21 January. The current laws on organized crime are largely a result of Russia's inability to deal with this problem, according to Natalia Lopashenko, head of the TraCCC program in Saratov. Almost the only area of agreement among the scholars, law enforcement agents, and judges was that the level of organized crime is rising. Figures from the Interior Ministry suggest that the number of economic crimes, in particular, is shooting upward.
    [Show full text]
  • Packing by Edge Disjoint Trees
    Global Journal of Mathematical Sciences: Theory and Practical. ISSN 0974-3200 Volume 5, Number 4 (2013), pp. 245_250 © International Research Publication House http://www.irphouse.com Packing by Edge Disjoint Trees Elachini V. Lal1 and Karakkattu S. Parvathy2 1Dept. of Higher Secondary, Govt. HSS Kuttippuram, Kerala INDIA– 679571. [email protected] 2Dept. of Mathematics, St. Mary’s College, Thrissur, Kerala INDIA – 680020. [email protected] Abstract A Graph G is said to be a packing by edge disjoint trees, if its edges can be partitioned into trees. In this paper, we discuss the packability of graphs of various types by edge disjoint tree and find its number w (edt G) and its least number wl (edt G) Key Words: Packing, Edge disjoint trees. 1. Introduction: By a graph G = (V, E) we mean a finite, undirected, connected graph with no loop or multiple edges. The order and size of G are denoted by ‘m’ and ‘n’ respectively. For basic graph theoretic terminology, we refer to [1, 2, 3]. The concept of random packability was introduced by Sergio Ruiz [4] under the name of ‘random decomposable graphs’. Ruiz [4] obtained a characterization of randomly F- packable graphs, when F is P3 or K2. Lowell W Beineke [5] and Peter Hamburger [5] and Wayne D Goddard [5] characterized F-packable graphs where F is Kn, P4, P5, or P6. S.Arumugham [6] and S.Meena [6] extended a characterization of the random packability of two or more disconnected graphs like Kn U K1, n, C4 U P2 ,3K2 .Elachini V. Lal [7] and Karakkattu S.
    [Show full text]
  • Spindown Polyhedra
    Spindown Polyhedra ANTHONY F. CONSTANTINIDES and GEORGE A. CONSTANTINIDES ARTICLE HISTORY Compiled March 20, 2018 1. Introduction Magic: The Gathering is a trading card game published by Wizards of the Coast [1]. The aim of most variants of the game is to reduce your opponent's life total from twenty to zero, thus winning the game. As it may take several turns to reduce a player's life total to zero, players need a mechanism to keep track of their current life total. For this purpose, players often use a device called a spindown life counter, shown in Figure 1. A spindown life counter is an icosahedron with a special labelling of the faces, such that - starting with 20 life total - a player can reduce their life total in decrements of one by rolling the icosahedron onto an adjacent face each time. A spindown life counter appears similar to a standard icosahedral die, known in gaming as a d20, however, the labelling of faces is different, as also shown in Figure 1. Figure 1. Left: A spindown life counter from Magic: The Gathering. Right: A standard icosahedral die (d20). The first author posed the question of whether it is possible to construct other polyhedra having a similar `spindown' property. Some simple experimentation revealed that is it possible to re-label the faces of a standard six-faced die (d6) to produce a spindown cube (see Figure 2); further experimentation revealed this to be the case for all Platonic solids. It can also be seen that it is possible, in all these cases, to chose the labelling such that it is not only spindown but also the face with the lowest label adjacent to the face with the highest label.
    [Show full text]
  • Putin's Syrian Gambit: Sharper Elbows, Bigger Footprint, Stickier Wicket
    STRATEGIC PERSPECTIVES 25 Putin’s Syrian Gambit: Sharper Elbows, Bigger Footprint, Stickier Wicket by John W. Parker Center for Strategic Research Institute for National Strategic Studies National Defense University Institute for National Strategic Studies National Defense University The Institute for National Strategic Studies (INSS) is National Defense University’s (NDU’s) dedicated research arm. INSS includes the Center for Strategic Research, Center for Complex Operations, Center for the Study of Chinese Military Affairs, and Center for Technology and National Security Policy. The military and civilian analysts and staff who comprise INSS and its subcomponents execute their mission by conducting research and analysis, publishing, and participating in conferences, policy support, and outreach. The mission of INSS is to conduct strategic studies for the Secretary of Defense, Chairman of the Joint Chiefs of Staff, and the unified combatant commands in support of the academic programs at NDU and to perform outreach to other U.S. Government agencies and the broader national security community. Cover: Admiral Kuznetsov aircraft carrier, August, 2012 (Russian Ministry of Defense) Putin's Syrian Gambit Putin's Syrian Gambit: Sharper Elbows, Bigger Footprint, Stickier Wicket By John W. Parker Institute for National Strategic Studies Strategic Perspectives, No. 25 Series Editor: Denise Natali National Defense University Press Washington, D.C. July 2017 Opinions, conclusions, and recommendations expressed or implied within are solely those of the contributors and do not necessarily represent the views of the Defense Department or any other agency of the Federal Government. Cleared for public release; distribution unlimited. Portions of this work may be quoted or reprinted without permission, provided that a standard source credit line is included.
    [Show full text]
  • List Coloring Under Some Graph Operations 1
    Kragujevac Journal of Mathematics Volume 46(3) (2022), Pages 417–431. LIST COLORING UNDER SOME GRAPH OPERATIONS KINKAR CHANDRA DAS1, SAMANE BAKAEIN2, MOSTAFA TAVAKOLI2∗, FREYDOON RAHBARNIA2, AND ALIREZA ASHRAFI3 Abstract. The list coloring of a graph G = G(V, E) is to color each vertex v ∈ V (G) from its color set L(v). If any two adjacent vertices have different colors, then G is properly colored. The aim of this paper is to study the list coloring of some graph operations. 1. Introduction Throughout this paper, our notations are standard and can be taken from the famous book of West [16]. The set of all positive integers is denoted by N, and for a set X, the power set of X is denoted by P (X). All graphs are assumed to be simple and finite, and if G is such a graph, then its vertex and edge sets are denoted by V (G) and E(G), respectively. The graph coloring is an important concept in modern graph theory with many applications in computer science. A function α : V (G) → N is called a coloring for G. The coloring α is said to be proper, if for each edge uv ∈ E(G), α(u) 6= α(v). If the coloring α uses only the colors [k] = {1, 2, . , k}, then α is called a k-coloring for G, and if such a proper k-coloring exists, then the graph G is said to be k-colorable. The smallest possible number k for which the graph G is k-colorable is the chromatic number of G and is denoted by χ(G).
    [Show full text]