LEADER 05021nam 2200721 a 450 001 9910954453803321 005 20240514064807.0 010 $a9786613621443 010 $a9781118205594 010 $a1118205596 010 $a9781280591617 010 $a1280591617 010 $a9781118205563 010 $a1118205561 035 $a(CKB)2670000000160771 035 $a(EBL)817847 035 $a(OCoLC)780445286 035 $a(SSID)ssj0000636036 035 $a(PQKBManifestationID)12252919 035 $a(PQKBTitleCode)TC0000636036 035 $a(PQKBWorkID)10660474 035 $a(PQKB)11553919 035 $a(MiAaPQ)EBC817847 035 $a(Au-PeEL)EBL817847 035 $a(CaPaEBR)ebr10540916 035 $a(CaONFJC)MIL362144 035 $a(Perlego)2768700 035 $a(EXLCZ)992670000000160771 100 $a20111018d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aGraph edge coloring $eVizing's theorem and Goldberg's conjecture /$fMichael Stiebitz ... [et al.] 205 $a1st ed. 210 $aHoboken, N.J. $cWiley$d2012 215 $a1 online resource (339 p.) 225 1 $aWiley series in discrete mathematics and optimization 300 $aDescription based upon print version of record. 311 08$a9781118091371 311 08$a111809137X 320 $aIncludes bibliographical references and indexes. 327 $aGraph 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 327 $a4.2 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 327 $a6.1 Density and Fractional Chromatic Index6.2 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 ?' Depending on ? and ?; 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 327 $a8.4 The Fan Equation for the Chromatic Index ?'f8.5 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 ?'f*; References; Symbol Index; Name Index; Subject Index 330 $a"Written by world authorities on graph theory, this book features many new advances and applications in graph edge coloring, describes how the results are interconnected, and provides historial context throughout. Chapter coverage includes an introduction to coloring preliminaries and lower and upper bounds; the Vizing fan; the Kierstead path; simple graphs and line graphs of multigraphs; the Tashkinov tree; Goldberg's conjecture; extreme graphs; generalized edge coloring; and open problems. It serves as a reference for researchers interested in discrete mathematics, graph theory, operations research, theoretical computer science, and combinatorial optimization, as well as a graduate-level course book for students of mathematics, optimization, and computer science"--$cProvided by publisher. 410 0$aWiley series in discrete mathematics and optimization. 606 $aGraph coloring 606 $aGraph theory 615 0$aGraph coloring. 615 0$aGraph theory. 676 $a511/.56 686 $aMAT008000$2bisacsh 701 $aStiebitz$b Michael$f1954-$01689789 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910954453803321 996 $aGraph edge coloring$94361050 997 $aUNINA