Graph Coloring Problems

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Graph Coloring Problems

Tommy R. Jensen,Bjarne Toft
Graph Coloring Problems Book PDF

Author : Tommy R. Jensen,Bjarne Toft
Publisher : John Wiley & Sons
Page : 320 pages
File Size : 46,6 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118030745

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Graph Coloring Problems by Tommy R. Jensen,Bjarne Toft Pdf

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.

A Guide to Graph Colouring

R.M.R. Lewis
A Guide to Graph Colouring Book PDF

Author : R.M.R. Lewis
Publisher : Springer
Page : 253 pages
File Size : 43,9 Mb
Release : 2015-10-26
Category : Computers
ISBN : 9783319257303

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A Guide to Graph Colouring by R.M.R. Lewis Pdf

This 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.

Graph Colorings

Marek Kubale
Graph Colorings Book PDF

Author : Marek Kubale
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 43,8 Mb
Release : 2004
Category : Graph coloring
ISBN : 9780821834589

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Graph Colorings by Marek Kubale Pdf

Graph coloring is one of the oldest and best-known problems of graph theory. As people grew accustomed to applying the tools of graph theory to the solutions of real-world technological and organizational problems, new chromatic models emerged as a natural way of tackling many practical situations. Statistics show that graph coloring is one of the central issues in the collection of several hundred classical combinatorial problems. This book is devoted to problems in graph coloring,which can be viewed as one area of discrete optimization. Chapters are dedicated to various models and are largely independent of one another. In each chapter, the author highlights algorithmic aspects of the presented models, i.e., the construction of polynomial-time algorithms for graph coloring.This is an expanded and updated translation of the prizewinning book originally published in Polish, Optymalizacja dyskretna. Modele i metody kolorowania grafow. It is suitable for graduate students and researchers interested in graph theory.

Graph Colouring and the Probabilistic Method

Michael Molloy,Bruce Reed
Graph Colouring and the Probabilistic Method Book PDF

Author : Michael Molloy,Bruce Reed
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 44,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783642040160

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Graph Colouring and the Probabilistic Method by Michael Molloy,Bruce Reed Pdf

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.

Graph Colouring and Applications

Pierre Hansen,Odile Marcotte
Graph Colouring and Applications Book PDF

Author : Pierre Hansen,Odile Marcotte
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 45,6 Mb
Release : 1999
Category : Mathematics
ISBN : 0821819550

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Graph Colouring and Applications by Pierre Hansen,Odile Marcotte Pdf

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.

Distributed Graph Coloring

Leonid Barenboim,Michael Elkin
Distributed Graph Coloring Book PDF

Author : Leonid Barenboim,Michael Elkin
Publisher : Springer Nature
Page : 157 pages
File Size : 54,6 Mb
Release : 2022-06-01
Category : Computers
ISBN : 9783031020094

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Distributed Graph Coloring by Leonid Barenboim,Michael Elkin Pdf

The focus of this monograph is on symmetry breaking problems in the message-passing model of distributed computing. In this model a communication network is represented by a n-vertex graph G = (V,E), whose vertices host autonomous processors. The processors communicate over the edges of G in discrete rounds. The goal is to devise algorithms that use as few rounds as possible. A typical symmetry-breaking problem is the problem of graph coloring. Denote by ? the maximum degree of G. While coloring G with ? + 1 colors is trivial in the centralized setting, the problem becomes much more challenging in the distributed one. One can also compromise on the number of colors, if this allows for more efficient algorithms. Other typical symmetry-breaking problems are the problems of computing a maximal independent set (MIS) and a maximal matching (MM). The study of these problems dates back to the very early days of distributed computing. The founding fathers of distributed computing laid firm foundations for the area of distributed symmetry breaking already in the eighties. In particular, they showed that all these problems can be solved in randomized logarithmic time. Also, Linial showed that an O(?2)-coloring can be solved very efficiently deterministically. However, fundamental questions were left open for decades. In particular, it is not known if the MIS or the (? + 1)-coloring can be solved in deterministic polylogarithmic time. Moreover, until recently it was not known if in deterministic polylogarithmic time one can color a graph with significantly fewer than ?2 colors. Additionally, it was open (and still open to some extent) if one can have sublogarithmic randomized algorithms for the symmetry breaking problems. Recently, significant progress was achieved in the study of these questions. More efficient deterministic and randomized (? + 1)-coloring algorithms were achieved. Deterministic ?1 + o(1)-coloring algorithms with polylogarithmic running time were devised. Improved (and often sublogarithmic-time) randomized algorithms were devised. Drastically improved lower bounds were given. Wide families of graphs in which these problems are solvable much faster than on general graphs were identified. The objective of our monograph is to cover most of these developments, and as a result to provide a treatise on theoretical foundations of distributed symmetry breaking in the message-passing model. We hope that our monograph will stimulate further progress in this exciting area.

Color-Induced Graph Colorings

Ping Zhang
Color Induced Graph Colorings Book PDF

Author : Ping Zhang
Publisher : Springer
Page : 118 pages
File Size : 54,5 Mb
Release : 2015-08-10
Category : Mathematics
ISBN : 9783319203942

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Color-Induced Graph Colorings by Ping Zhang Pdf

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.

Proceedings of the International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA) 2013

Suresh Chandra Satapathy,Siba K Udgata,Bhabendra Narayan Biswal
Proceedings of the International Conference on Frontiers of Intelligent Computing Theory and Applications FICTA 2013 Book PDF

Author : Suresh Chandra Satapathy,Siba K Udgata,Bhabendra Narayan Biswal
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 42,5 Mb
Release : 2013-10-05
Category : Technology & Engineering
ISBN : 9783319029313

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Proceedings of the International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA) 2013 by Suresh Chandra Satapathy,Siba K Udgata,Bhabendra Narayan Biswal Pdf

This volume contains the papers presented at the Second International Conference on Frontiers in Intelligent Computing: Theory and Applications (FICTA-2013) held during 14-16 November 2013 organized by Bhubaneswar Engineering College (BEC), Bhubaneswar, Odisha, India. It contains 63 papers focusing on application of intelligent techniques which includes evolutionary computation techniques like genetic algorithm, particle swarm optimization techniques, teaching-learning based optimization etc for various engineering applications such as data mining, Fuzzy systems, Machine Intelligence and ANN, Web technologies and Multimedia applications and Intelligent computing and Networking etc.

Mathematical Foundations of Computer Science 2004

Jirí Fiala,Václav Koubek,Jan Kratochvíl
Mathematical Foundations of Computer Science 2004 Book PDF

Author : Jirí Fiala,Václav Koubek,Jan Kratochvíl
Publisher : Springer Science & Business Media
Page : 916 pages
File Size : 51,5 Mb
Release : 2004-08-09
Category : Computers
ISBN : 9783540228233

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Mathematical Foundations of Computer Science 2004 by Jirí Fiala,Václav Koubek,Jan Kratochvíl Pdf

This volume contains the papers presented at the 29th Symposium on Mat- matical Foundations of Computer Science, MFCS 2004, held in Prague, Czech Republic, August 22–27, 2004. The conference was organized by the Institute for Theoretical Computer Science (ITI) and the Department of Theoretical Com- terScienceandMathematicalLogic(KTIML)oftheFacultyofMathematicsand Physics of Charles University in Prague. It was supported in part by the Eu- pean Association for Theoretical Computer Science (EATCS) and the European Research Consortium for Informatics and Mathematics (ERCIM). Traditionally, the MFCS symposia encourage high-quality research in all branches of theoretical computer science. Ranging in scope from automata, f- mal languages, data structures, algorithms and computational geometry to c- plexitytheory,modelsofcomputation,andapplicationsincludingcomputational biology, cryptography, security and arti?cial intelligence, the conference o?ers a unique opportunity to researchers from diverse areas to meet and present their results to a general audience. The scienti?c program of this year’s MFCS took place in the lecture halls of the recently reconstructed building of the Faculty of Mathematics and P- sics in the historical center of Prague, with the famous Prague Castle and other celebratedhistoricalmonumentsinsight.Theviewfromthewindowswasach- lengingcompetitionforthespeakersinthe?ghtfortheattentionoftheaudience. But we did not fear the result: Due to the unusually tough competition for this year’s MFCS, the admitted presentations certainly attracted considerable in- rest. The conference program (and the proceedings) consisted of 60 contributed papers selected by the Program Committee from a total of 167 submissions.

Chromatic Graph Theory

Gary Chartrand,Ping Zhang
Chromatic Graph Theory Book PDF

Author : Gary Chartrand,Ping Zhang
Publisher : CRC Press
Page : 504 pages
File Size : 48,8 Mb
Release : 2008-09-22
Category : Mathematics
ISBN : 1584888016

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Chromatic Graph Theory by Gary Chartrand,Ping Zhang Pdf

Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents 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. The remainder of the text deals exclusively with graph colorings. It 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, and many distance-related vertex colorings. With historical, applied, and algorithmic discussions, this text offers a solid introduction to one of the most popular areas of graph theory.

Graphs on Surfaces

Bojan Mohar,Carsten Thomassen
Graphs on Surfaces Book PDF

Author : Bojan Mohar,Carsten Thomassen
Publisher : Johns Hopkins University Press
Page : 0 pages
File Size : 54,8 Mb
Release : 2001-08-02
Category : Mathematics
ISBN : 0801866898

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Graphs on Surfaces by Bojan Mohar,Carsten Thomassen Pdf

Graph theory is one of the fastest growing branches of mathematics. Until recently, it was regarded as a branch of combinatorics and was best known by the famous four-color theorem stating that any map can be colored using only four colors such that no two bordering countries have the same color. Now graph theory is an area of its own with many deep results and beautiful open problems. Graph theory has numerous applications in almost every field of science and has attracted new interest because of its relevance to such technological problems as computer and telephone networking and, of course, the internet. In this new book in the Johns Hopkins Studies in the Mathematical Science series, Bojan Mohar and Carsten Thomassen look at a relatively new area of graph theory: that associated with curved surfaces. Graphs on surfaces form a natural link between discrete and continuous mathematics. The book provides a rigorous and concise introduction to graphs on surfaces and surveys some of the recent developments in this area. Among the basic results discussed are Kuratowski's theorem and other planarity criteria, the Jordan Curve Theorem and some of its extensions, the classification of surfaces, and the Heffter-Edmonds-Ringel rotation principle, which makes it possible to treat graphs on surfaces in a purely combinatorial way. The genus of a graph, contractability of cycles, edge-width, and face-width are treated purely combinatorially, and several results related to these concepts are included. The extension by Robertson and Seymour of Kuratowski's theorem to higher surfaces is discussed in detail, and a shorter proof is presented. The book concludes with a survey of recent developments on coloring graphs on surfaces.

Handbook of Optimization

Ivan Zelinka,Vaclav Snasael,Ajith Abraham
Handbook of Optimization Book PDF

Author : Ivan Zelinka,Vaclav Snasael,Ajith Abraham
Publisher : Springer Science & Business Media
Page : 1100 pages
File Size : 46,7 Mb
Release : 2012-09-26
Category : Technology & Engineering
ISBN : 9783642305047

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Handbook of Optimization by Ivan Zelinka,Vaclav Snasael,Ajith Abraham Pdf

Optimization problems were and still are the focus of mathematics from antiquity to the present. Since the beginning of our civilization, the human race has had to confront numerous technological challenges, such as finding the optimal solution of various problems including control technologies, power sources construction, applications in economy, mechanical engineering and energy distribution amongst others. These examples encompass both ancient as well as modern technologies like the first electrical energy distribution network in USA etc. Some of the key principles formulated in the middle ages were done by Johannes Kepler (Problem of the wine barrels), Johan Bernoulli (brachystochrone problem), Leonhard Euler (Calculus of Variations), Lagrange (Principle multipliers), that were formulated primarily in the ancient world and are of a geometric nature. In the beginning of the modern era, works of L.V. Kantorovich and G.B. Dantzig (so-called linear programming) can be considered amongst others. This book discusses a wide spectrum of optimization methods from classical to modern, alike heuristics. Novel as well as classical techniques is also discussed in this book, including its mutual intersection. Together with many interesting chapters, a reader will also encounter various methods used for proposed optimization approaches, such as game theory and evolutionary algorithms or modelling of evolutionary algorithm dynamics like complex networks.

Algorithms - ESA 2007

Lars Arge,Michael Hoffmann,Emo Welzl
Algorithms ESA 2007 Book PDF

Author : Lars Arge,Michael Hoffmann,Emo Welzl
Publisher : Springer
Page : 772 pages
File Size : 46,7 Mb
Release : 2007-09-17
Category : Computers
ISBN : 9783540755203

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Algorithms - ESA 2007 by Lars Arge,Michael Hoffmann,Emo Welzl Pdf

This book constitutes the refereed proceedings of the 15th Annual European Symposium on Algorithms, ESA 2007, held in Eilat, Israel, in October 2007 in the context of the combined conference ALGO 2007. The 63 revised full papers presented together with abstracts of three invited lectures address all current subjects in algorithmics reaching from design and analysis issues of algorithms over to real-world applications and engineering of algorithms in various fields.

The Mathematical Coloring Book

Alexander Soifer
The Mathematical Coloring Book Book PDF

Author : Alexander Soifer
Publisher : Springer Science & Business Media
Page : 619 pages
File Size : 45,9 Mb
Release : 2008-10-13
Category : Mathematics
ISBN : 9780387746425

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The Mathematical Coloring Book by Alexander Soifer Pdf

This 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.

Discrete Mathematics

Oscar Levin
Discrete Mathematics Book PDF

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
Page : 238 pages
File Size : 54,6 Mb
Release : 2018-07-30
Category : Electronic
ISBN : 1724572636

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Discrete Mathematics by Oscar Levin Pdf

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.