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| Preface | |
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| Introduction | |
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| Graphs | |
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| Coloring Preliminaries | |
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| Critical Graphs | |
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| Lower Bounds and Elementary Graphs | |
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| Upper Bounds and Coloring Algorithms | |
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| Notes | |
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| Vizing Fans | |
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| The Fan Equation and the Classical Bounds | |
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| Adjacency Lemmas | |
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| The Second Fan Equation | |
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| The Double Fan | |
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| The Fan Number | |
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| Notes | |
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| Kierstead Paths | |
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| Kierstead's Method | |
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| Short Kierstead's Paths | |
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| Notes | |
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| Simple Graphs and Line Graphs | |
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| Class One and Class Two Graphs | |
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| Graphs whose Core has Maximum Degree Two | |
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| Simple Overfull Graphs | |
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| Adjacency Lemmas for Critical Class Two Graphs | |
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| Average Degree of Critical Class Two Graphs | |
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| Independent Vertices in Critical Class Two Graphs | |
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| Constructions of Critical Class Two Graphs | |
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| Hadwiger's Conjecture for Line Graphs | |
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| Simple Graphs on Surfaces | |
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| Notes | |
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| Tashkinov Trees | |
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| Tashkinov's Method | |
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| Extended Tashkinov Trees | |
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| Asymptotic Bounds | |
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| Tashkinov's Coloring Algorithm | |
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| Polynomial Time Algorithms | |
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| Notes | |
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| Goldberg's Conjecture | |
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| Density and Fractional Chromatic Index | |
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| Balanced Tashkinov Trees | |
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| Obstructions | |
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| Approximation Algorithms | |
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| Goldberg's Conjecture for Small Graphs | |
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| Another Classification Problem for Graphs | |
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| Notes | |
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| Extreme Graphs | |
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| Shannon's Bound and Ring Graphs | |
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| Vizing's Bound and Extreme Graphs | |
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| Extreme Graphs and Elementary Graphs | |
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| Upper Bounds for �' Depending on � and � | |
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| Notes | |
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| Generalized Edge Colorings of Graphs | |
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| Equitable and Balanced Edge Colorings | |
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| Full Edge Colorings and the Cover Index | |
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| Edge Colorings of Weighted Graphs | |
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| The Fan Equation for the Chromatic Index �<sup>′</sup><sub>f</sub> | |
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| Decomposing Graphs into Simple Graphs | |
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| Notes | |
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| Twenty Pretty Edge Coloring Conjectures | |
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| Vizing's Two Fundamental Papers | |
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| On an Estimate of the Chromatic Class of a p-Graph | |
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| References | |
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| Critical Graphs with a Given Chromatic Class | |
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| References | |
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| Fractional Edge Colorings | |
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| The Fractional Chromatic Index | |
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| The Matching Polytope | |
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| A Formula for �<sup>′*</sup><sub>f</sub> | |
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| References | |
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| Symbol Index | |
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| Name Index | |
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| Subject Index | |