05266nam 2200637 450 991083067110332120230421053750.01-283-33198-597866133319841-118-03249-71-118-03074-5(CKB)2670000000133154(EBL)695948(OCoLC)768230300(SSID)ssj0000554814(PQKBManifestationID)11356212(PQKBTitleCode)TC0000554814(PQKBWorkID)10517363(PQKB)10010730(MiAaPQ)EBC695948(EXLCZ)99267000000013315420160816h19951995 uy 0engur|n|---|||||txtccrGraph coloring problems /Tommy R. Jensen, Bjarne ToftNew York, New York :John Wiley & Sons, Inc.,1995.©19951 online resource (324 p.)Wiley-Interscience Series in Discrete Mathematics and Optimization"A Wiley-Interscience Publication."0-471-02865-7 Includes bibliographical references at the end of each chapters and indexes.Graph Coloring Problems; Contents; Preface; 1 Introduction to Graph Coloring; 1.1 Basic Definitions; 1.2 Graphs on Surfaces; 1.3 Vertex Degrees and Colorings; 1.4 Criticality and Complexity; 16.14 Partition Problem of Galvin and Hajnal; 1.5 Sparse Graphs and Random Graphs; 1.6 Perfect Graphs; 1.7 Edge-Coloring; 1.8 Orientations and Integer Flows; 1.9 List Coloring; 1.10 Generalized Graph Coloring; 1.11 Final Remarks; Bibliography; 2 Planar Graphs; 2.1 Four-Color Theorem; 2.2 Cartesian Sequences; 2.3 Intersection Graphs of Planar Segments; 2.4 Ringerl's Earth-Moon Problem2.5 Ore and Plummer's Cyclic Chromatic Number2.6 Vertex Partitionings w.r.t. Coloring Number; 2.7 Vertex Partitionings w.r.t. Maximum Degree; 2.8 The Three-Color Problem; 2.9 Steinberg's Three-Color Problem; 2.10 Grünbaum and Havel's Three-Color Problem; 2.11 Grötzsch and Sachs' Three-Color Problem; 2.12 Barnette's Conjecture; 2.13 List-Coloring Planar Graphs; 2.14 Kronk and Mitchem's Entire Chromatic Number; 2.15 Nine-Color Conjecture; 2.16 Uniquely Colorable Graphs; 2.17 Density of 4-Critical Planar Graphs; 2.18 Square of Planar Graphs; Bibliography; 3 Graphs on Higher Surfaces3.1 Heawood's Empire Problem3.2 Grünbaum's 3-Edge-Color Conjecture; 3.3 Albertson's Four-Color Problem; 3.4 Improper Colorings; 3.5 Number of 6-Critical Graphs on a Surface; 3.6 Toroidal Polyhedra; 3.7 Polynomial Coloring of Embedded Graphs; 3.8 Sparse Embedded Graphs; 3.9 Ringel's 1-Chromatic Number; 3.10 Borodin's Conjecture on Diagonal Coloring; 3.11 Acyclic Colorings; 3.12 Cochromatic Numbers; 3.13 Graphs on Pseudo-Surfaces; Bibliography; 4 Degrees; 4.1 The Coloring Number; 4.2 Coloring of Decomposable Graphs; 4.3 Color-Bound Families of Graphs; 4.4 Edge-Disjoint Placements4.5 Powers of Hamilton Cycles4.6 Brooks' Theorem for Triangle-Free Graphs; 4.7 Graphs Without Large Complete Subgraphs; 4.8 k-Chromatic Graphs of Maximum Degree k; 4.9 Total Coloring; 4.10 Equitable Coloring; 4.11 Acyclic Coloring; 4.12 Melnikov's Valency-Variety Problem; 4.13 Induced-Odd Degree Subgraphs; 4.14 Strong Chromatic Number; Bibliography; 5 Critical Graphs; 5.1 Critical Graphs With Many Edges; 5.2 Minimum Degree of 4- and 5-Critical Graphs; 5.3 Critical Graphs With Few Edges; 5.4 Four-Critical Amenable Graphs; 5.5 Four-Critical Degree 5 Problem5.6 Large Critical Subgraphs of Critical Graphs5.7 Critical Subgraph Covering a 2-Path; 5.8 Noninduced Critical Subgraphs; 5.9 Number of Critical Subgraphs; 5.10 Subgraphs of Critical Graphs; 5.11 Minimal Circumference of Critical Graphs; 5.12 The Erdös-Lovász Tihany Problem; 5.13 Partial Joins of Critical Graphs; 5.14 Vertex-Critical Graphs Without Critical Edges; Bibliography; 6 The Conjectures of Hadwiger and Hajós; 6.1 Hadwiger's Conjecture; 6.2 Hajós' Conjecture; 6.3 The (m, n)- and [m, n]-Conjectures; 6.4 Hadwiger Degree of a Graph; 6.5 Graphs Without Odd-K5; 6.6 Scheme Conjecture6.7 Chromatic 4-SchemesContains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.Wiley-Interscience series in discrete mathematics and optimization.Graph coloringGraph coloring.511.5511/.5Jensen Tommy R.753649Toft BjarneMiAaPQMiAaPQMiAaPQBOOK9910830671103321Graph coloring problems1516178UNINA