Graphs On Surfaces

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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 : 47,6 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.

Graphs on Surfaces and Their Applications

Sergei K. Lando,Alexander K. Zvonkin
Graphs on Surfaces and Their Applications Book PDF

Author : Sergei K. Lando,Alexander K. Zvonkin
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 44,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783540383611

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Graphs on Surfaces and Their Applications by Sergei K. Lando,Alexander K. Zvonkin Pdf

Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Graphs on Surfaces

Joanna A. Ellis-Monaghan,Iain Moffatt
Graphs on Surfaces Book PDF

Author : Joanna A. Ellis-Monaghan,Iain Moffatt
Publisher : Springer Science & Business Media
Page : 139 pages
File Size : 52,9 Mb
Release : 2013-06-28
Category : Mathematics
ISBN : 9781461469711

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Graphs on Surfaces by Joanna A. Ellis-Monaghan,Iain Moffatt Pdf

Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.

Graphs, Surfaces and Homology

Peter Giblin
Graphs Surfaces and Homology Book PDF

Author : Peter Giblin
Publisher : Cambridge University Press
Page : 273 pages
File Size : 48,5 Mb
Release : 2010-08-12
Category : Mathematics
ISBN : 9781139491174

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Graphs, Surfaces and Homology by Peter Giblin Pdf

Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.

Graphs, Groups and Surfaces

A.T. White
Graphs Groups and Surfaces Book PDF

Author : A.T. White
Publisher : Elsevier
Page : 313 pages
File Size : 41,6 Mb
Release : 1985-01-01
Category : Mathematics
ISBN : 0080871194

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Graphs, Groups and Surfaces by A.T. White Pdf

The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing. Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'' and 9 as ``unsolved''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''.

Pearls in Graph Theory

Nora Hartsfield,Gerhard Ringel
Pearls in Graph Theory Book PDF

Author : Nora Hartsfield,Gerhard Ringel
Publisher : Courier Corporation
Page : 272 pages
File Size : 53,8 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9780486315522

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Pearls in Graph Theory by Nora Hartsfield,Gerhard Ringel Pdf

Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.

Configurations from a Graphical Viewpoint

Tomaz Pisanski,Brigitte Servatius
Configurations from a Graphical Viewpoint Book PDF

Author : Tomaz Pisanski,Brigitte Servatius
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 51,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9780817683634

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Configurations from a Graphical Viewpoint by Tomaz Pisanski,Brigitte Servatius Pdf

Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. In this self-contained textbook, algebraic graph theory is used to introduce groups; topological graph theory is used to explore surfaces; and geometric graph theory is implemented to analyze incidence geometries. After a preview of configurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5 introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied. Geometric aspects, some historical remarks, references, and applications of classical configurations appear in the last chapter. With over two hundred illustrations, challenging exercises at the end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint is well suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicians and researchers.

Topological Theory of Graphs

Yanpei Liu
Topological Theory of Graphs Book PDF

Author : Yanpei Liu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 424 pages
File Size : 50,7 Mb
Release : 2017-03-06
Category : Mathematics
ISBN : 9783110479225

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Topological Theory of Graphs by Yanpei Liu Pdf

This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid, and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of MacLane (on cycle bases), and of Whitney (on duality) for planarity. Relevant problems include the Jordan axiom in polyhedral forms, efficient methods for extremality and for recognizing a variety of embeddings (including rectilinear layouts in VLSI), and pan-polynomials, including those of Jones, Kauffman (on knots), and Tutte (on graphs), among others. Contents Preliminaries Polyhedra Surfaces Homology on Polyhedra Polyhedra on the Sphere Automorphisms of a Polyhedron Gauss Crossing Sequences Cohomology on Graphs Embeddability on Surfaces Embeddings on Sphere Orthogonality on Surfaces Net Embeddings Extremality on Surfaces Matroidal Graphicness Knot Polynomials

The Foundations of Topological Graph Theory

C.Paul Bonnington,Charles H.C. Little
The Foundations of Topological Graph Theory Book PDF

Author : C.Paul Bonnington,Charles H.C. Little
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461225409

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The Foundations of Topological Graph Theory by C.Paul Bonnington,Charles H.C. Little Pdf

This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced.

Topics in Topological Graph Theory

Lowell W. Beineke,Robin J. Wilson
Topics in Topological Graph Theory Book PDF

Author : Lowell W. Beineke,Robin J. Wilson
Publisher : Cambridge University Press
Page : 366 pages
File Size : 44,9 Mb
Release : 2009-07-09
Category : Mathematics
ISBN : 052180230X

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Topics in Topological Graph Theory by Lowell W. Beineke,Robin J. Wilson Pdf

The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.

Graphs, Algorithms, and Optimization, Second Edition

William Kocay,Donald L. Kreher
Graphs Algorithms and Optimization Second Edition Book PDF

Author : William Kocay,Donald L. Kreher
Publisher : CRC Press
Page : 543 pages
File Size : 48,8 Mb
Release : 2016-11-03
Category : Mathematics
ISBN : 9781482251258

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Graphs, Algorithms, and Optimization, Second Edition by William Kocay,Donald L. Kreher Pdf

The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs. ?

Map Color Theorem

G. Ringel
Map Color Theorem Book PDF

Author : G. Ringel
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642657597

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Map Color Theorem by G. Ringel Pdf

In 1890 P. J. Heawood [35] published a formula which he called the Map Colour Theorem. But he forgot to prove it. Therefore the world of mathematicians called it the Heawood Conjecture. In 1968 the formula was proven and therefore again called the Map Color Theorem. (This book is written in California, thus in American English. ) Beautiful combinatorial methods were developed in order to prove the formula. The proof is divided into twelve cases. In 1966 there were three of them still unsolved. In the academic year 1967/68 J. W. T. Youngs on those three cases at Santa Cruz. Sur invited me to work with him prisingly our joint effort led to the solution of all three cases. It was a year of hard work but great pleasure. Working together was extremely profitable and enjoyable. In spite of the fact that we saw each other every day, Ted wrote a letter to me, which I present here in shortened form: Santa Cruz, March 1, 1968 Dear Gerhard: Last night while I was checking our results on Cases 2, 8 and 11, and thinking of the great pleasure we had in the afternoon with the extra ordinarily elegant new solution for Case 11, it seemed to me appropriate to pause for a few minutes and dictate a historical memorandum. We began working on Case 8 on 10 October 1967, and it was settled on Tuesday night, 14 November 1967.

Modern Graph Theory

Bela Bollobas
Modern Graph Theory Book PDF

Author : Bela Bollobas
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 54,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461206194

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Modern Graph Theory by Bela Bollobas Pdf

An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.

Introduction to Graph Theory

Koh Khee Meng,Dong Fengming,Tay Eng Guan
Introduction to Graph Theory Book PDF

Author : Koh Khee Meng,Dong Fengming,Tay Eng Guan
Publisher : World Scientific Publishing Company
Page : 244 pages
File Size : 51,9 Mb
Release : 2007-03-15
Category : Mathematics
ISBN : 9789813101630

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Introduction to Graph Theory by Koh Khee Meng,Dong Fengming,Tay Eng Guan Pdf

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.

Chromatic Graph Theory

Gary Chartrand,Ping Zhang
Chromatic Graph Theory Book PDF

Author : Gary Chartrand,Ping Zhang
Publisher : CRC Press
Page : 503 pages
File Size : 53,7 Mb
Release : 2019-11-28
Category : Mathematics
ISBN : 9780429798283

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Chromatic Graph Theory by Gary Chartrand,Ping Zhang Pdf

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