Topics In Gallai Ramsey Theory
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Topics In Gallai Ramsey Theory
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Author : Colton Magnant
language : en
Publisher: Springer Nature
Release Date : 2020-07-04
Topics In Gallai Ramsey Theory written by Colton Magnant and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-04 with Mathematics categories.
This book explores topics in Gallai-Ramsey theory, which looks into whether rainbow colored subgraphs or monochromatic subgraphs exist in a sufficiently large edge-colored complete graphs. A comprehensive survey of all known results with complete references is provided for common proof methods. Fundamental definitions and preliminary results with illustrations guide readers to comprehend recent innovations. Complete proofs and influential results are discussed with numerous open problems and conjectures. Researchers and students with an interest in edge-coloring, Ramsey Theory, and colored subgraphs will find this book a valuable guide for entering Gallai-Ramsey Theory.
Star Critical Ramsey Numbers For Graphs
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Author : Mark R. Budden
language : en
Publisher: Springer Nature
Release Date : 2023-05-13
Star Critical Ramsey Numbers For Graphs written by Mark R. Budden and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-13 with Mathematics categories.
This text is a comprehensive survey of the literature surrounding star-critical Ramsey numbers. First defined by Jonelle Hook in her 2010 dissertation, these numbers aim to measure the sharpness of the corresponding Ramsey numbers by determining the minimum number of edges needed to be added to a critical graph for the Ramsey property to hold. Despite being in its infancy, the topic has gained significant attention among Ramsey theorists. This work provides researchers and students with a resource for studying known results and their complete proofs. It covers typical results, including multicolor star-critical Ramsey numbers for complete graphs, trees, cycles, wheels, and n-good graphs, among others. The proofs are streamlined and, in some cases, simplified, with a few new results included. The book also explores the connection between star-critical Ramsey numbers and deleted edge numbers, which focus on destroying the Ramsey property by removing edges. The book concludes with open problems and conjectures for researchers to consider, making it a valuable resource for those studying the field of star-critical Ramsey numbers.
Chromatic Graph Theory
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Author : Gary Chartrand
language : en
Publisher: CRC Press
Release Date : 2019-11-28
Chromatic Graph Theory written by Gary Chartrand and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-28 with Mathematics categories.
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
Combinatorics And Graph Theory
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Author : John Harris
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Combinatorics And Graph Theory written by John Harris and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Mathematics categories.
There are certain rules that one must abide by in order to create a successful sequel. — Randy Meeks, from the trailer to Scream 2 While we may not follow the precise rules that Mr. Meeks had in mind for s- cessful sequels, we have made a number of changes to the text in this second edition. In the new edition, we continue to introduce new topics with concrete - amples, we provide complete proofs of almost every result, and we preserve the book’sfriendlystyle andlivelypresentation,interspersingthetextwith occasional jokes and quotations. The rst two chapters, on graph theory and combinatorics, remain largely independent, and may be covered in either order. Chapter 3, on in nite combinatorics and graphs, may also be studied independently, although many readers will want to investigate trees, matchings, and Ramsey theory for nite sets before exploring these topics for in nite sets in the third chapter. Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well. It assumes only familiarity with basic proof techniques, and some experience with matrices and in nite series. The second edition offersmany additionaltopics for use in the classroom or for independentstudy. Chapter 1 includesa new sectioncoveringdistance andrelated notions in graphs, following an expanded introductory section. This new section also introduces the adjacency matrix of a graph, and describes its connection to important features of the graph.
Topics In Combinatorics And Graph Theory
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Author : R. Rama
language : en
Publisher: Springer Nature
Release Date : 2025-07-01
Topics In Combinatorics And Graph Theory written by R. Rama and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-01 with Mathematics categories.
The book covers all the basics of both the topics. The topics are sequenced in such a manner that there is a flow in understanding the advances. The first and second chapters cover all the basic methods and tools for counting. Chapter 3 is on binomial theorem and binomial identities. Topics such as partitions, permutations on multisets, generating functions, recurrence relation, principle of inclusion exclusion, repeated counting, partially ordered sets and Mobius inversion, Polya's counting are covered in different chapters. Some basic chapters have some worked-out exercise. Information on Catalan numbers, Eulerian Numbers, Narayana Numbers, and Schroder Number are given in a chapter. The topic on "discrete probability" covers the connection between counting techniques and probability theory. There second part of the book covers topics in graph theory such as basics of graphs, trees,bipartite graphs, matching , planar graphs, Euler and Hamilton graphs, graph coloring, Ramsey theory, spectral properties, and some graph algorithms.Adequate exercise and examples are provided so as to enhance the reader's interest and understanding. Some interesting concepts like high hamiltonicity, power of graphs, domination, and matrix tree theorem are introduced.
The Mathematical Coloring Book
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Author : Alexander Soifer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-13
The Mathematical Coloring Book written by Alexander Soifer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-13 with Mathematics categories.
This is a unique type of book; at least, I have never encountered a book of this kind. The best description of it I can give is that it is a mystery novel, developing on three levels, and imbued with both educational and philosophical/moral issues. If this summary description does not help understanding the particular character and allure of the book, possibly a more detailed explanation will be found useful. One of the primary goals of the author is to interest readers—in particular, young mathematiciansorpossiblypre-mathematicians—inthefascinatingworldofelegant and easily understandable problems, for which no particular mathematical kno- edge is necessary, but which are very far from being easily solved. In fact, the prototype of such problems is the following: If each point of the plane is to be given a color, how many colors do we need if every two points at unit distance are to receive distinct colors? More than half a century ago it was established that the least number of colorsneeded for such a coloring is either 4, or 5, or 6 or 7. Well, which is it? Despite efforts by a legion of very bright people—many of whom developed whole branches of mathematics and solved problems that seemed much harder—not a single advance towards the answer has been made. This mystery, and scores of other similarly simple questions, form one level of mysteries explored. In doing this, the author presents a whole lot of attractive results in an engaging way, and with increasing level of depth.
Topics On Domination
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Author : S.T. Hedetniemi
language : en
Publisher: Elsevier
Release Date : 1991-02-01
Topics On Domination written by S.T. Hedetniemi and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-02-01 with Mathematics categories.
The contributions in this volume are divided into three sections: theoretical, new models and algorithmic. The first section focuses on properties of the standard domination number &ggr;(G), the second section is concerned with new variations on the domination theme, and the third is primarily concerned with finding classes of graphs for which the domination number (and several other domination-related parameters) can be computed in polynomial time.
Chromatic Graph Theory
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Author : Gary Chartrand
language : en
Publisher: CRC Press
Release Date : 2019-11-28
Chromatic Graph Theory written by Gary Chartrand and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-28 with Mathematics categories.
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 Theory And Related Topics
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Author : W. T. Tutte
language : en
Publisher: New York : Academic Press
Release Date : 1979
Graph Theory And Related Topics written by W. T. Tutte and has been published by New York : Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Early reminiscences; A tribute; A note on some of professor Tutte's mathematical work; Papers and books by W.T. Tutte; Topological and algebraic methods in graph theory; All the king's horses; Hadwiger's conjecture and six-chromatic toroidal graphs; Planar colorings: a theory.
Combinatorial Mathematics
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Author : Douglas B. West
language : en
Publisher: Cambridge University Press
Release Date : 2021
Combinatorial Mathematics written by Douglas B. West and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
This is the most readable and thorough graduate textbook and reference for combinatorics, covering enumeration, graphs, sets, and methods.