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Author: Marek Kubale
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 224
ISBN-13: 0821834584
DOWNLOAD EBOOKGraph 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.
Author: Michael Molloy
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 320
ISBN-13: 3642040160
DOWNLOAD EBOOKOver 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.
Author: R.M.R. Lewis
Publisher: Springer
Published: 2015-10-26
Total Pages: 256
ISBN-13: 3319257307
DOWNLOAD EBOOKThis book treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses some of the best-known algorithms for colouring arbitrary graphs, focusing on whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. The introductory chapters explain graph colouring, and bounds and constructive algorithms. The author then shows how advanced, modern techniques can be applied to classic real-world operational research problems such as seating plans, sports scheduling, and university timetabling. He includes many examples, suggestions for further reading, and historical notes, and the book is supplemented by a website with an online suite of downloadable code. The book will be of value to researchers, graduate students, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence. The reader should have elementary knowledge of sets, matrices, and enumerative combinatorics.
Author: Tommy R. Jensen
Publisher: John Wiley & Sons
Published: 2011-10-24
Total Pages: 320
ISBN-13: 1118030745
DOWNLOAD EBOOKContains 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.
Author: Ping Zhang
Publisher: Springer
Published: 2015-08-10
Total Pages: 130
ISBN-13: 3319203940
DOWNLOAD EBOOKA 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.
Author: Hian Poh Yap
Publisher: Springer
Published: 2006-11-13
Total Pages: 140
ISBN-13: 3540493018
DOWNLOAD EBOOKThis book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.
Author: Robert A. Wilson
Publisher: OUP Oxford
Published: 2002-01-24
Total Pages: 153
ISBN-13: 019158360X
DOWNLOAD EBOOKThe four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.
Author: Gary Chartrand
Publisher: CRC Press
Published: 2019-11-28
Total Pages: 526
ISBN-13: 0429798288
DOWNLOAD EBOOKWith 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
Author: Alexander Soifer
Publisher: Springer Science & Business Media
Published: 2008-10-13
Total Pages: 619
ISBN-13: 0387746420
DOWNLOAD EBOOKThis book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdös, B.L. van der Waerden, and Henry Baudet.
Author: Michael Stiebitz
Publisher: John Wiley & Sons
Published: 2012-02-27
Total Pages: 344
ISBN-13: 1118205561
DOWNLOAD EBOOKFeatures 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.
