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Author:   Michael Stiebitz ,  Diego Scheide ,  Bjarne Toft ,  Lene M. Favrholdt
Publisher:   John Wiley & Sons Inc
Imprint:   John Wiley & Sons Inc
Volume:   75
Dimensions:   Width: 16.30cm , Height: 2.50cm , Length: 23.60cm
Weight:   0.635kg
ISBN:  

9781118091371

ISBN 10:   111809137
Pages:   344
Publication Date:   02 March 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Preface xi 1 Introduction 1 1.1 Graphs 1 1.2 Coloring Preliminaries 2 1.3 Critical Graphs 5 1.4 Lower Bounds and Elementary Graphs 6 1.5 Upper Bounds and Coloring Algorithms 11 1.6 Notes 15 2 Vizing Fans 19 2.1 The Fan Equation and the Classical Bounds 19 2.2 Adjacency Lemmas 24 2.3 The Second Fan Equation 26 2.4 The Double Fan 31 2.5 The Fan Number 32 2.6 Notes 39 3 Kierstead Paths 43 3.1 Kierstead's Method 43 3.2 Short Kierstead's Paths 46 3.3 Notes 49 4 Simple Graphs and Line Graphs 51 4.1 Class One and Class Two Graphs 51 4.2 Graphs whose Core has Maximum Degree Two 54 4.3 Simple Overfull Graphs 63 4.4 Adjacency Lemmas for Critical Class Two Graphs 73 4.5 Average Degree of Critical Class Two Graphs 84 4.6 Independent Vertices in Critical Class Two Graphs 89 4.7 Constructions of Critical Class Two Graphs 93 4.8 Hadwiger's Conjecture for Line Graphs 101 4.9 Simple Graphs on Surfaces 105 4.10 Notes 110 5 Tashkinov Trees 115 5.1 Tashkinov's Method 115 5.2 Extended Tashkinov Trees 127 5.3 Asymptotic Bounds 139 5.4 Tashkinov's Coloring Algorithm 144 5.5 Polynomial Time Algorithms 148 5.6 Notes 152 6 Goldberg's Conjecture 155 6.1 Density and Fractional Chromatic Index 155 6.2 Balanced Tashkinov Trees 160 6.3 Obstructions 162 6.4 Approximation Algorithms 183 6.5 Goldberg's Conjecture for Small Graphs 185 6.6 Another Classification Problem for Graphs 186 6.7 Notes 193 7 Extreme Graphs 197 7.1 Shannon's Bound and Ring Graphs 197 7.2 Vizing's Bound and Extreme Graphs 201 7.3 Extreme Graphs and Elementary Graphs 203 7.4 Upper Bounds for ÷' Depending on Ä and ì 205 7.5 Notes 209 8 Generalized Edge Colorings of Graphs 213 8.1 Equitable and Balanced Edge Colorings 213 8.2 Full Edge Colorings and the Cover Index 222 8.3 Edge Colorings of Weighted Graphs 224 8.4 The Fan Equation for the Chromatic Index X'f  228 8.5 Decomposing Graphs into Simple Graphs 239 8.6 Notes 243 9 Twenty Pretty Edge Coloring Conjectures 245 Appendix A: Vizing's Two Fundamental Papers 269 A. 1 On an Estimate of the Chromatic Class of a p-Graph 269 References 272 A.2 Critical Graphs with a Given Chromatic Class 273 References 278 Appendix B: Fractional Edge Colorings 281 B. 1 The Fractional Chromatic Index 281 B.2 The Matching Polytope 284 B.3 A Formula for X'f  290 References 295 Symbol Index 312 Name Index 314 Subject Index 318

Reviews

College mathematics collections need just this sort of rarity-accounts of major unsolved problems, elementary but still comprehensive. Summing Up: Recommended. Upper-division undergraduates. ( Choice , 1 September 2012)

Author Information

Michael Stiebitz, PhD, is Professor of Mathematics at the Technical University of Ilmenau, Germany. He is the author of numerous journal articles in his areas of research interest, which include graph theory, combinatorics, cryptology, and linear algebra. Diego Scheide, PhD, is a Postdoctoral Researcher in the Department of Mathematics at Simon Fraser University, Canada. Bjarne Toft, PhD, is Associate Professor in the Department of Mathematics and Computer Science at the University of Southern Denmark. Lene M. Favrholdt, PhD, is Associate Professor in the Department of Mathematics and Computer Science at the University of Southern Denmark.

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