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.


Book Synopsis Color-Induced Graph Colorings by : Ping Zhang

Download or read book Color-Induced Graph Colorings written by Ping Zhang and published by Springer. This book was released on 2015-08-10 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Kaleidoscopic View of Graph Colorings

A Kaleidoscopic View of Graph Colorings

Author: Ping Zhang

Publisher: Springer

Published: 2016-03-30

Total Pages: 160

ISBN-13: 3319305182

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This book describes kaleidoscopic topics that have developed in the area of graph colorings. Unifying current material on graph coloring, this book describes current information on vertex and edge colorings in graph theory, including harmonious colorings, majestic colorings, kaleidoscopic colorings and binomial colorings. Recently there have been a number of breakthroughs in vertex colorings that give rise to other colorings in a graph, such as graceful labelings of graphs that have been reconsidered under the language of colorings. The topics presented in this book include sample detailed proofs and illustrations, which depicts elements that are often overlooked. This book is ideal for graduate students and researchers in graph theory, as it covers a broad range of topics and makes connections between recent developments and well-known areas in graph theory.


Book Synopsis A Kaleidoscopic View of Graph Colorings by : Ping Zhang

Download or read book A Kaleidoscopic View of Graph Colorings written by Ping Zhang and published by Springer. This book was released on 2016-03-30 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes kaleidoscopic topics that have developed in the area of graph colorings. Unifying current material on graph coloring, this book describes current information on vertex and edge colorings in graph theory, including harmonious colorings, majestic colorings, kaleidoscopic colorings and binomial colorings. Recently there have been a number of breakthroughs in vertex colorings that give rise to other colorings in a graph, such as graceful labelings of graphs that have been reconsidered under the language of colorings. The topics presented in this book include sample detailed proofs and illustrations, which depicts elements that are often overlooked. This book is ideal for graduate students and researchers in graph theory, as it covers a broad range of topics and makes connections between recent developments and well-known areas in graph theory.

Extremal Problems on Induced Graph Colorings

Extremal Problems on Induced Graph Colorings

Author: James Hallas

Publisher:

Published: 2020

Total Pages: 118

ISBN-13:

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Graph coloring is one of the most popular areas of graph theory, no doubt due to its many fascinating problems and applications to modern society, as well as the sheer mathematical beauty of the subject. As far back as 1880, in an attempt to solve the famous Four Color Problem, there have been numerous examples of certain types of graph colorings that have generated other graph colorings of interest. These types of colorings only gained momentum a century later, however, when in the 1980s, edge colorings were studied that led to vertex colorings of various types, led by the introduction of the irregularity strength of a graph by Chartrand and the majestic chromatic index of a graph by Harary and Plantholt. Since then, the study of such graph colorings has become a popular area of research in graph theory. Recently, two set and number theoretic graph colorings were introduced, namely royal colorings and rainbow mean colorings. These two colorings as well as variations have extended some classical graph coloring concepts. We investigate structural and extremal problems dealing with royal and rainbow mean colorings and explore relationships among the chromatic parameters resulting from these colorings and traditional chromatic parameters.


Book Synopsis Extremal Problems on Induced Graph Colorings by : James Hallas

Download or read book Extremal Problems on Induced Graph Colorings written by James Hallas and published by . This book was released on 2020 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph coloring is one of the most popular areas of graph theory, no doubt due to its many fascinating problems and applications to modern society, as well as the sheer mathematical beauty of the subject. As far back as 1880, in an attempt to solve the famous Four Color Problem, there have been numerous examples of certain types of graph colorings that have generated other graph colorings of interest. These types of colorings only gained momentum a century later, however, when in the 1980s, edge colorings were studied that led to vertex colorings of various types, led by the introduction of the irregularity strength of a graph by Chartrand and the majestic chromatic index of a graph by Harary and Plantholt. Since then, the study of such graph colorings has become a popular area of research in graph theory. Recently, two set and number theoretic graph colorings were introduced, namely royal colorings and rainbow mean colorings. These two colorings as well as variations have extended some classical graph coloring concepts. We investigate structural and extremal problems dealing with royal and rainbow mean colorings and explore relationships among the chromatic parameters resulting from these colorings and traditional chromatic parameters.

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.


Book Synopsis Graph Colorings by : Marek Kubale

Download or read book Graph Colorings written by Marek Kubale and published by American Mathematical Soc.. This book was released on 2004 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.


Book Synopsis Graph Coloring Problems by : Tommy R. Jensen

Download or read book Graph Coloring Problems written by Tommy R. Jensen and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graph Colouring and Applications

Graph Colouring and Applications

Author: Pierre Hansen

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 168

ISBN-13: 9780821819555

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This volume presents the proceedings of the CRM workshop on graph coloring and applications. The articles span a wide spectrum of topics related to graph coloring, including: list-colorings, total colorings, colorings and embeddings of graphs, chromatic polynomials, characteristic polynomials, chromatic scheduling, and graph coloring problems related to frequency assignment. Outstanding researchers in combinatorial optimization and graph theory contributed their work. A list of open problems is included.


Book Synopsis Graph Colouring and Applications by : Pierre Hansen

Download or read book Graph Colouring and Applications written by Pierre Hansen and published by American Mathematical Soc.. This book was released on 1999 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the CRM workshop on graph coloring and applications. The articles span a wide spectrum of topics related to graph coloring, including: list-colorings, total colorings, colorings and embeddings of graphs, chromatic polynomials, characteristic polynomials, chromatic scheduling, and graph coloring problems related to frequency assignment. Outstanding researchers in combinatorial optimization and graph theory contributed their work. A list of open problems is included.

Chromatic Graph Theory

Chromatic Graph Theory

Author: Gary Chartrand

Publisher: CRC Press

Published: 2019-11-28

Total Pages: 450

ISBN-13: 042979827X

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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


Book Synopsis Chromatic Graph Theory by : Gary Chartrand

Download or read book Chromatic Graph Theory written by Gary Chartrand and published by CRC Press. This book was released on 2019-11-28 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Coloring Mixed Hypergraphs: Theory, Algorithms and Applications

Coloring Mixed Hypergraphs: Theory, Algorithms and Applications

Author: Vitaly Ivanovich Voloshin

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 199

ISBN-13: 0821828126

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The theory of graph coloring has existed for more than 150 years. Historically, graph coloring involved finding the minimum number of colors to be assigned to the vertices so that adjacent vertices would have different colors. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications. Generalization of graph coloring-type problems to mixed hypergraphs brings many new dimensions to the theory ofcolorings. A main feature of this book is that in the case of hypergraphs, there exist problems on both the minimum and the maximum number of colors. This feature pervades the theory, methods, algorithms, and applications of mixed hypergraph coloring. The book has broad appeal. It will be of interest to bothpure and applied mathematicians, particularly those in the areas of discrete mathematics, combinatorial optimization, operations research, computer science, software engineering, molecular biology, and related businesses and industries. It also makes a nice supplementary text for courses in graph theory and discrete mathematics. This is especially useful for students in combinatorics and optimization. Since the area is new, students will have the chance at this stage to obtain results that maybecome classic in the future.


Book Synopsis Coloring Mixed Hypergraphs: Theory, Algorithms and Applications by : Vitaly Ivanovich Voloshin

Download or read book Coloring Mixed Hypergraphs: Theory, Algorithms and Applications written by Vitaly Ivanovich Voloshin and published by American Mathematical Soc.. This book was released on 2002 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of graph coloring has existed for more than 150 years. Historically, graph coloring involved finding the minimum number of colors to be assigned to the vertices so that adjacent vertices would have different colors. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications. Generalization of graph coloring-type problems to mixed hypergraphs brings many new dimensions to the theory ofcolorings. A main feature of this book is that in the case of hypergraphs, there exist problems on both the minimum and the maximum number of colors. This feature pervades the theory, methods, algorithms, and applications of mixed hypergraph coloring. The book has broad appeal. It will be of interest to bothpure and applied mathematicians, particularly those in the areas of discrete mathematics, combinatorial optimization, operations research, computer science, software engineering, molecular biology, and related businesses and industries. It also makes a nice supplementary text for courses in graph theory and discrete mathematics. This is especially useful for students in combinatorics and optimization. Since the area is new, students will have the chance at this stage to obtain results that maybecome classic in the future.

Total Colourings of Graphs

Total Colourings of Graphs

Author: Hian Poh Yap

Publisher: Springer

Published: 2006-11-13

Total Pages: 140

ISBN-13: 3540493018

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This 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.


Book Synopsis Total Colourings of Graphs by : Hian Poh Yap

Download or read book Total Colourings of Graphs written by Hian Poh Yap and published by Springer. This book was released on 2006-11-13 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.

Handbook of Combinatorial Optimization

Handbook of Combinatorial Optimization

Author: Ding-Zhu Du

Publisher: Springer Science & Business Media

Published: 2006-08-18

Total Pages: 395

ISBN-13: 0387238301

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This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.


Book Synopsis Handbook of Combinatorial Optimization by : Ding-Zhu Du

Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.