Graph edge coloring : Vizing's theorem and Goldberg's conjecture /

"This book provides an overview of this development as well as describes how the many different results are related"--

Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Stiebitz, Michael, 1954-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Hoboken, NJ : Wiley, 2012.
Colección:Wiley series in discrete mathematics and optimization.
Temas:
Graph coloring.
Graph theory.
MATHEMATICS > Discrete Mathematics.
Coloriage de graphes.
MATHEMATICS > Graphic Methods.
Graph coloring
Graph theory
Acceso en línea:Texto completo

MARC

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245 0 0 |a Graph edge coloring :  |b Vizing's theorem and Goldberg's conjecture /  |c Michael Stiebitz [and others]. 
260 |a Hoboken, NJ :  |b Wiley,  |c 2012. 
300 |a 1 online resource (xiv, 321 pages) :  |b illustrations 
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490 1 |a Wiley series in discrete mathematics and optimization 
500 |a "Written by world authorities on graph theory, this book features many new advances and applications in graph edge coloring, describes how the results are interconnected, and provides historial context throughout. Chapter coverage includes an introduction to coloring preliminaries and lower and upper bounds; the Vizing fan; the Kierstead path; simple graphs and line graphs of multigraphs; the Tashkinov tree; Goldberg's conjecture; extreme graphs; generalized edge coloring; and open problems. It serves as a reference for researchers interested in discrete mathematics, graph theory, operations research, theoretical computer science, and combinatorial optimization, as well as a graduate-level course book for students of mathematics, optimization, and computer science"--Provided by publisher 
520 |a "This book provides an overview of this development as well as describes how the many different results are related"--  |c Provided by publisher 
504 |a Includes bibliographical references and indexes. 
588 0 |a Print version record. 
505 0 |a Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture; CONTENTS; Preface; 1 Introduction; 1.1 Graphs; 1.2 Coloring Preliminaries; 1.3 Critical Graphs; 1.4 Lower Bounds and Elementary Graphs; 1.5 Upper Bounds and Coloring Algorithms; 1.6 Notes; 2 Vizing Fans; 2.1 The Fan Equation and the Classical Bounds; 2.2 Adjacency Lemmas; 2.3 The Second Fan Equation; 2.4 The Double Fan; 2.5 The Fan Number; 2.6 Notes; 3 Kierstead Paths; 3.1 Kierstead's Method; 3.2 Short Kierstead's Paths; 3.3 Notes; 4 Simple Graphs and Line Graphs; 4.1 Class One and Class Two Graphs 
505 8 |a 4.2 Graphs whose Core has Maximum Degree Two4.3 Simple Overfull Graphs; 4.4 Adjacency Lemmas for Critical Class Two Graphs; 4.5 Average Degree of Critical Class Two Graphs; 4.6 Independent Vertices in Critical Class Two Graphs; 4.7 Constructions of Critical Class Two Graphs; 4.8 Hadwiger's Conjecture for Line Graphs; 4.9 Simple Graphs on Surfaces; 4.10 Notes; 5 Tashkinov Trees; 5.1 Tashkinov's Method; 5.2 Extended Tashkinov Trees; 5.3 Asymptotic Bounds; 5.4 Tashkinov's Coloring Algorithm; 5.5 Polynomial Time Algorithms; 5.6 Notes; 6 Goldberg's Conjecture 
546 |a English. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Graph coloring. 
650 0 |a Graph theory. 
650 4 |a MATHEMATICS  |x Discrete Mathematics. 
650 4 |a Graph theory. 
650 4 |a Graph coloring. 
650 6 |a Coloriage de graphes. 
650 7 |a MATHEMATICS  |x Discrete Mathematics.  |2 bisacsh 
650 7 |a MATHEMATICS  |x Graphic Methods.  |2 bisacsh 
650 7 |a Graph coloring  |2 fast 
650 7 |a Graph theory  |2 fast 
700 1 |a Stiebitz, Michael,  |d 1954-  |1 https://id.oclc.org/worldcat/entity/E39PCjCrRVqHMvk3hBrRjtrMGd 
758 |i has work:  |a Graph edge coloring (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGytwF9mcdB8Xbp7jhW79C  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |t Graph edge coloring.  |d Hoboken, NJ : Wiley, 2012  |z 9781118091371  |w (DLC) 2011038045  |w (OCoLC)747529203 
830 0 |a Wiley series in discrete mathematics and optimization. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=817847  |z Texto completo 
880 0 |6 505-00/(S  |a Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture -- CONTENTS -- Preface -- 1 Introduction -- 1.1 Graphs -- 1.2 Coloring Preliminaries -- 1.3 Critical Graphs -- 1.4 Lower Bounds and Elementary Graphs -- 1.5 Upper Bounds and Coloring Algorithms -- 1.6 Notes -- 2 Vizing Fans -- 2.1 The Fan Equation and the Classical Bounds -- 2.2 Adjacency Lemmas -- 2.3 The Second Fan Equation -- 2.4 The Double Fan -- 2.5 The Fan Number -- 2.6 Notes -- 3 Kierstead Paths -- 3.1 Kierstead's Method -- 3.2 Short Kierstead's Paths -- 3.3 Notes -- 4 Simple Graphs and Line Graphs -- 4.1 Class One and Class Two Graphs -- 4.2 Graphs whose Core has Maximum Degree Two -- 4.3 Simple Overfull Graphs -- 4.4 Adjacency Lemmas for Critical Class Two Graphs -- 4.5 Average Degree of Critical Class Two Graphs -- 4.6 Independent Vertices in Critical Class Two Graphs -- 4.7 Constructions of Critical Class Two Graphs -- 4.8 Hadwiger's Conjecture for Line Graphs -- 4.9 Simple Graphs on Surfaces -- 4.10 Notes -- 5 Tashkinov Trees -- 5.1 Tashkinov's Method -- 5.2 Extended Tashkinov Trees -- 5.3 Asymptotic Bounds -- 5.4 Tashkinov's Coloring Algorithm -- 5.5 Polynomial Time Algorithms -- 5.6 Notes -- 6 Goldberg's Conjecture -- 6.1 Density and Fractional Chromatic Index -- 6.2 Balanced Tashkinov Trees -- 6.3 Obstructions -- 6.4 Approximation Algorithms -- 6.5 Goldberg's Conjecture for Small Graphs -- 6.6 Another Classification Problem for Graphs -- 6.7 Notes -- 7 Extreme Graphs -- 7.1 Shannon's Bound and Ring Graphs -- 7.2 Vizing's Bound and Extreme Graphs -- 7.3 Extreme Graphs and Elementary Graphs -- 7.4 Upper Bounds for χ' Depending on Δ and μ -- 7.5 Notes -- 8 Generalized Edge Colorings of Graphs -- 8.1 Equitable and Balanced Edge Colorings -- 8.2 Full Edge Colorings and the Cover Index -- 8.3 Edge Colorings of Weighted Graphs. 
880 8 |6 505-00/(S  |a 8.4 The Fan Equation for the Chromatic Index χ'f -- 8.5 Decomposing Graphs into Simple Graphs -- 8.6 Notes -- 9 Twenty Pretty Edge Coloring Conjectures -- Appendix A: Vizing's Two Fundamental Papers -- A.1 On an Estimate of the Chromatic Class of a p-Graph -- References -- A.2 Critical Graphs with a Given Chromatic Class -- References -- Appendix B: Fractional Edge Colorings -- B.1 The Fractional Chromatic Index -- B.2 The Matching Polytope -- B.3 A Formula for χ'f* -- References -- Symbol Index -- Name Index -- Subject Index. 
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