{"product_id":"graph-edge-coloring-9781118091371","title":"Graph Edge Coloring","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eFeatures recent advances and new applications in graph edge coloring\u003c\/b\u003e  \u003cp\u003eReviewing recent advances in the Edge Coloring Problem, \u003ci\u003eGraph Edge Coloring: Vizing''s Theorem and Goldberg''s Conjecture\u003c\/i\u003e provides an overview of the current state of the science, explaining the interconnections among the results obtained from important graph theory studies. The authors introduce many new improved proofs of known results to identify and point to possible solutions for open problems in edge coloring.\u003c\/p\u003e \u003cp\u003eThe book begins with an introduction to graph theory and the concept of edge coloring. Subsequent chapters explore important topics such as:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eUse of Tashkinov trees to obtain an asymptotic positive solution to Goldberg''s conjecture\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eApplication of Vizing fans to obtain both known and new results\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eKierstead paths as an alternative to Vizing fans\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eClassification problem of simple graphs\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eGeneralized \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\n\u003cp\u003e“College mathematics collections need just this sort of rarity-accounts of major unsolved problems, elementary but still comprehensive.  Summing Up: Recommended.  Upper-division undergraduates.”  (\u003ci\u003eChoice\u003c\/i\u003e, 1 September 2012)\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi  \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Graphs 1\u003c\/p\u003e \u003cp\u003e1.2 Coloring Preliminaries 2\u003c\/p\u003e \u003cp\u003e1.3 Critical Graphs 5\u003c\/p\u003e \u003cp\u003e1.4 Lower Bounds and Elementary Graphs 6\u003c\/p\u003e \u003cp\u003e1.5 Upper Bounds and Coloring Algorithms 11\u003c\/p\u003e \u003cp\u003e1.6 Notes 15\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Vizing Fans 19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Fan Equation and the Classical Bounds 19\u003c\/p\u003e \u003cp\u003e2.2 Adjacency Lemmas 24\u003c\/p\u003e \u003cp\u003e2.3 The Second Fan Equation 26\u003c\/p\u003e \u003cp\u003e2.4 The Double Fan 31\u003c\/p\u003e \u003cp\u003e2.5 The Fan Number 32\u003c\/p\u003e \u003cp\u003e2.6 Notes 39\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Kierstead Paths 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Kierstead's Method 43\u003c\/p\u003e \u003cp\u003e3.2 Short Kierstead's Paths 46\u003c\/p\u003e \u003cp\u003e3.3 Notes 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Simple Graphs and Line Graphs 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Class One and Class Two Graphs 51\u003c\/p\u003e \u003cp\u003e4.2 Graphs whose Core has Maximum Degree Two 54\u003c\/p\u003e \u003cp\u003e4.3 Simple Overfull Graphs 63\u003c\/p\u003e \u003cp\u003e4.4 Adjacency Lemmas for Critical Class Two Graphs 73\u003c\/p\u003e \u003cp\u003e4.5 Average Degree of Critical Class Two Graphs 84\u003c\/p\u003e \u003cp\u003e4.6 Independent Vertices in Critical Class Two Graphs 89\u003c\/p\u003e \u003cp\u003e4.7 Constructions of Critical Class Two Graphs 93\u003c\/p\u003e \u003cp\u003e4.8 Hadwiger's Conjecture for Line Graphs 101\u003c\/p\u003e \u003cp\u003e4.9 Simple Graphs on Surfaces 105\u003c\/p\u003e \u003cp\u003e4.10 Notes 110\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Tashkinov Trees 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Tashkinov's Method 115\u003c\/p\u003e \u003cp\u003e5.2 Extended Tashkinov Trees 127\u003c\/p\u003e \u003cp\u003e5.3 Asymptotic Bounds 139\u003c\/p\u003e \u003cp\u003e5.4 Tashkinov's Coloring Algorithm 144\u003c\/p\u003e \u003cp\u003e5.5 Polynomial Time Algorithms 148\u003c\/p\u003e \u003cp\u003e5.6 Notes 152\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Goldberg's Conjecture 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Density and Fractional Chromatic Index 155\u003c\/p\u003e \u003cp\u003e6.2 Balanced Tashkinov Trees 160\u003c\/p\u003e \u003cp\u003e6.3 Obstructions 162\u003c\/p\u003e \u003cp\u003e6.4 Approximation Algorithms 183\u003c\/p\u003e \u003cp\u003e6.5 Goldberg's Conjecture for Small Graphs 185\u003c\/p\u003e \u003cp\u003e6.6 Another Classification Problem for Graphs 186\u003c\/p\u003e \u003cp\u003e6.7 Notes 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Extreme Graphs 197\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Shannon's Bound and Ring Graphs 197\u003c\/p\u003e \u003cp\u003e7.2 Vizing's Bound and Extreme Graphs 201\u003c\/p\u003e \u003cp\u003e7.3 Extreme Graphs and Elementary Graphs 203\u003c\/p\u003e \u003cp\u003e7.4 Upper Bounds for \u003ci\u003e÷'\u003c\/i\u003e Depending on Ä and \u003ci\u003eì\u003c\/i\u003e 205\u003c\/p\u003e \u003cp\u003e7.5 Notes 209\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Generalized Edge Colorings of Graphs 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Equitable and Balanced Edge Colorings 213\u003c\/p\u003e \u003cp\u003e8.2 Full Edge Colorings and the Cover Index 222\u003c\/p\u003e \u003cp\u003e8.3 Edge Colorings of Weighted Graphs 224\u003c\/p\u003e \u003cp\u003e8.4 The Fan Equation for the Chromatic Index \u003ci\u003eX'f\u003c\/i\u003e\u003ci\u003e \u003c\/i\u003e 228\u003c\/p\u003e \u003cp\u003e8.5 Decomposing Graphs into Simple Graphs 239\u003c\/p\u003e \u003cp\u003e8.6 Notes 243\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Twenty Pretty Edge Coloring Conjectures 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A: Vizing's Two Fundamental Papers 269\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA. 1 On an Estimate of the Chromatic Class of a p-Graph 269\u003c\/p\u003e \u003cp\u003eReferences 272\u003c\/p\u003e \u003cp\u003eA.2 Critical Graphs with a Given Chromatic Class 273\u003c\/p\u003e \u003cp\u003eReferences 278\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B: Fractional Edge Colorings 281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB. 1 The Fractional Chromatic Index 281\u003c\/p\u003e \u003cp\u003eB.2 The Matching Polytope 284\u003c\/p\u003e \u003cp\u003eB.3 A Formula for \u003ci\u003eX'f\u003c\/i\u003e\u003ci\u003e \u003c\/i\u003e 290\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences 295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSymbol Index 312\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eName Index 314\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSubject Index 318\u003c\/b\u003e\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406828544343,"sku":"9781118091371","price":90.86,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118091371.jpg?v=1730497255","url":"https:\/\/bookcurl.com\/products\/graph-edge-coloring-9781118091371","provider":"Book Curl","version":"1.0","type":"link"}