Graph Coloring Problems

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John Wiley & Sons, Oct 24, 2011 - Mathematics - 320 pages
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Contains 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.
 

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Contents

1 Introduction to Graph Coloring
1
2 Planar Graphs
31
3 Graphs on Higher Surfaces
59
4 Degrees
77
5 Critical Graphs
97
6 The Conjectures of Hadwiger and Hajós
109
7 Sparse Graphs
122
8 Perfect Graphs
131
11 Constructions
180
12 Edge Colorings
190
13 Orientations and Flows
209
14 Chromatic Polynomials
220
15 Hypergraphs
231
16 Infinite Chromatic Graphs
251
17 Miscellaneous Problems
261
Author Index
277

9 Geometric and Combinatorial Graphs
150
10 Algorithms
168

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