Preface | p. xi |
Introduction | p. 1 |
Graphs | p. 1 |
Coloring Preliminaries | p. 2 |
Critical Graphs | p. 5 |
Lower Bounds and Elementary Graphs | p. 6 |
Upper Bounds and Coloring Algorithms | p. 11 |
Notes | p. 15 |
Vizing Fans | p. 19 |
The Fan Equation and the Classical Bounds | p. 19 |
Adjacency Lemmas | p. 24 |
The Second Fan Equation | p. 26 |
The Double Fan | p. 31 |
The Fan Number | p. 32 |
Notes | p. 39 |
Kierstead Paths | p. 43 |
Kierstead's Method | p. 43 |
Short Kierstead's Paths | p. 46 |
Notes | p. 49 |
Simple Graphs and Line Graphs | p. 51 |
Class One and Class Two Graphs | p. 51 |
Graphs whose Core has Maximum Degree Two | p. 54 |
Simple Overfull Graphs | p. 63 |
Adjacency Lemmas for Critical Class Two Graphs | p. 73 |
Average Degree of Critical Class Two Graphs | p. 84 |
Independent Vertices in Critical Class Two Graphs | p. 89 |
Constructions of Critical Class Two Graphs | p. 93 |
Hadwiger's Conjecture for Line Graphs | p. 101 |
Simple Graphs on Surfaces | p. 105 |
Notes | p. 110 |
Tashkinov Trees | p. 115 |
Tashkinov's Method | p. 115 |
Extended Tashkinov Trees | p. 127 |
Asymptotic Bounds | p. 139 |
Tashkinov's Coloring Algorithm | p. 144 |
Polynomial Time Algorithms | p. 148 |
Notes | p. 152 |
Goldberg's Conjecture | p. 155 |
Density and Fractional Chromatic Index | p. 155 |
Balanced Tashkinov Trees | p. 160 |
Obstructions | p. 162 |
Approximation Algorithms | p. 183 |
Goldberg's Conjecture for Small Graphs | p. 185 |
Another Classification Problem for Graphs | p. 186 |
Notes | p. 193 |
Extreme Graphs | p. 197 |
Shannon's Bound and Ring Graphs | p. 197 |
Vizing's Bound and Extreme Graphs | p. 201 |
Extreme Graphs and Elementary Graphs | p. 203 |
Upper Bounds for ¿' Depending on ¿ and ¿ | p. 205 |
Notes | p. 209 |
Generalized Edge Colorings of Graphs | p. 213 |
Equitable and Balanced Edge Colorings | p. 213 |
Full Edge Colorings and the Cover Index | p. 222 |
Edge Colorings of Weighted Graphs | p. 224 |
The Fan Equation for the Chromatic Index ¿′f | p. 228 |
Decomposing Graphs into Simple Graphs | p. 239 |
Notes | p. 243 |
Twenty Pretty Edge Coloring Conjectures | p. 245 |
Vizing's Two Fundamental Papers | p. 269 |
On an Estimate of the Chromatic Class of a p-Graph | p. 269 |
References | p. 272 |
Critical Graphs with a Given Chromatic Class | p. 273 |
References | p. 278 |
Fractional Edge Colorings | p. 281 |
The Fractional Chromatic Index | p. 281 |
The Matching Polytope | p. 284 |
A Formula for ¿′*f | p. 290 |
References | p. 295 |
Symbol Index | p. 312 |
Name Index | p. 314 |
Subject Index | p. 318 |
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