Graph Edge Coloring
Graph Edge Coloring

Author: Michael Stiebitz

Publisher: John Wiley & Sons

Published: 2012-02-27

Total Pages: 344

ISBN-13: 1118205561

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Features recent advances and new applications in graph edgecoloring Reviewing recent advances in the Edge Coloring Problem, GraphEdge Coloring: Vizing's Theorem and Goldberg's Conjectureprovides an overview of the current state of the science,explaining the interconnections among the results obtained fromimportant graph theory studies. The authors introduce many newimproved proofs of known results to identify and point to possiblesolutions for open problems in edge coloring. The book begins with an introduction to graph theory and theconcept of edge coloring. Subsequent chapters explore importanttopics such as: Use of Tashkinov trees to obtain an asymptotic positive solutionto Goldberg's conjecture Application of Vizing fans to obtain both known and newresults Kierstead paths as an alternative to Vizing fans Classification problem of simple graphs Generalized edge coloring in which a color may appear more thanonce at a vertex This book also features first-time English translations of twogroundbreaking papers written by Vadim Vizing on an estimate of thechromatic class of a p-graph and the critical graphs within a givenchromatic class. Written by leading experts who have reinvigorated research inthe field, Graph Edge Coloring is an excellent book formathematics, optimization, and computer science courses at thegraduate level. The book also serves as a valuable reference forresearchers interested in discrete mathematics, graph theory,operations research, theoretical computer science, andcombinatorial optimization.

Graph Colorings
Graph Colorings

Author: Marek Kubale

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 224

ISBN-13: 0821834584

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Graph coloring is one of the oldest and best-known problems of graph theory. Statistics show that graph coloring is one of the central issues in the collection of several hundred classical combinatorial problems. This book covers the problems in graph coloring, which can be viewed as one area of discrete optimization.

Color-Induced Graph Colorings
Color-Induced Graph Colorings

Author: Ping Zhang

Publisher: Springer

Published: 2015-08-10

Total Pages: 130

ISBN-13: 3319203940

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A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted, the resulting vertex colorings are either proper colorings or rainbow colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings. Since many of the concepts described in this book are relatively recent, the audience for this book is primarily mathematicians interested in learning some new areas of graph colorings as well as researchers and graduate students in the mathematics community, especially the graph theory community.

Graph Coloring Problems
Graph Coloring Problems

Author: Tommy R. Jensen

Publisher: John Wiley & Sons

Published: 2011-10-24

Total Pages: 320

ISBN-13: 1118030745

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Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.

Chromatic Graph Theory
Chromatic Graph Theory

Author: Gary Chartrand

Publisher: CRC Press

Published: 2019-11-28

Total Pages: 526

ISBN-13: 0429798288

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With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition

Graph Colouring and the Probabilistic Method
Graph Colouring and the Probabilistic Method

Author: Michael Molloy

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 320

ISBN-13: 3642040160

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Over the past decade, many major advances have been made in the field of graph coloring via the probabilistic method. This monograph, by two of the best on the topic, provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality.

Distributed Graph Coloring
Distributed Graph Coloring

Author: Leonid Barenboim

Publisher: Morgan & Claypool Publishers

Published: 2013-07-01

Total Pages: 173

ISBN-13: 1627050191

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The objective of our monograph is to cover the developments on the theoretical foundations of distributed symmetry breaking in the message-passing model. We hope that our monograph will stimulate further progress in this exciting area.

The Petersen Graph
The Petersen Graph

Author: D. A. Holton

Publisher: Cambridge University Press

Published: 1993-04-22

Total Pages: 367

ISBN-13: 0521435943

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The authors examine various areas of graph theory, using the prominent role of the Petersen graph as a unifying feature.

Topics in Chromatic Graph Theory
Topics in Chromatic Graph Theory

Author: Lowell W. Beineke

Publisher: Cambridge University Press

Published: 2015-05-07

Total Pages: 416

ISBN-13: 1316239853

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Chromatic graph theory is a thriving area that uses various ideas of 'colouring' (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such areas as computer networks, where colouring algorithms form an important feature. While other books cover portions of the material, no other title has such a wide scope as this one, in which acknowledged international experts in the field provide a broad survey of the subject. All fifteen chapters have been carefully edited, with uniform notation and terminology applied throughout. Bjarne Toft (Odense, Denmark), widely recognized for his substantial contributions to the area, acted as academic consultant. The book serves as a valuable reference for researchers and graduate students in graph theory and combinatorics and as a useful introduction to the topic for mathematicians in related fields.