Combinatorics and Graph Theory
Combinatorics and Graph Theory

Author: John Harris

Publisher: Springer Science & Business Media

Published: 2009-04-03

Total Pages: 392

ISBN-13: 0387797114

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These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Geometric Graphs and Arrangements
Geometric Graphs and Arrangements

Author: Stefan Felsner

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 179

ISBN-13: 3322803031

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Among the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and partly very recent results from the intersection of geometry, graph theory and combinatorics.

Discrete Geometry, Combinatorics and Graph Theory
Discrete Geometry, Combinatorics and Graph Theory

Author: Jin Akiyama

Publisher: Springer

Published: 2007-06-26

Total Pages: 298

ISBN-13: 3540706666

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This book constitutes the thoroughly refereed post-proceedings of the 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, held in Tianjin, China, as well as in Xi'an, China, in November 2005. The 30 revised full papers address all current issues in discrete algorithmic geometry, combinatorics and graph theory.

Thirty Essays on Geometric Graph Theory
Thirty Essays on Geometric Graph Theory

Author: János Pach

Publisher: Springer Science & Business Media

Published: 2012-12-15

Total Pages: 610

ISBN-13: 1461401100

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In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.

Graphs and Geometry
Graphs and Geometry

Author: László Lovász

Publisher: American Mathematical Soc.

Published: 2019-08-28

Total Pages: 458

ISBN-13: 1470450879

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Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that this geometry is crucial in engineering, for example, if you want to understand rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly connected to the graph-theoretic problem, a well-chosen geometric embedding has mathematical meaning and applications in proofs and algorithms. This book surveys a number of such connections between graph theory and geometry: among others, rubber band representations, coin representations, orthogonal representations, and discrete analytic functions. Applications are given in information theory, statistical physics, graph algorithms and quantum physics. The book is based on courses and lectures that the author has given over the last few decades and offers readers with some knowledge of graph theory, linear algebra, and probability a thorough introduction to this exciting new area with a large collection of illuminating examples and exercises.

Computational Discrete Mathematics
Computational Discrete Mathematics

Author: Sriram Pemmaraju

Publisher: Cambridge University Press

Published: 2009-10-15

Total Pages: 615

ISBN-13: 1107268710

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This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.

Forbidden Configurations in Discrete Geometry
Forbidden Configurations in Discrete Geometry

Author: David Eppstein

Publisher: Cambridge University Press

Published: 2018-05-17

Total Pages: 241

ISBN-13: 1108423914

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Unifies discrete and computational geometry by using forbidden patterns of points to characterize many of its problems.

Combinatorics and Finite Geometry
Combinatorics and Finite Geometry

Author: Steven T. Dougherty

Publisher: Springer Nature

Published: 2020-10-30

Total Pages: 374

ISBN-13: 3030563952

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This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.

Geometry and Discrete Mathematics
Geometry and Discrete Mathematics

Author: Benjamin Fine

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-08-22

Total Pages: 364

ISBN-13: 3110740788

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Fundamentals of mathematics are presented in the two-volume set in an exciting and pedagogically sound way. The present volume examines the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history. New: A chapter on discrete Morse theory and still more graph theory for solving further classical problems as the Travelling Salesman and Postman problem.

Handbook of Discrete and Computational Geometry
Handbook of Discrete and Computational Geometry

Author: Csaba D. Toth

Publisher: CRC Press

Published: 2017-11-22

Total Pages: 2354

ISBN-13: 1351645919

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The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.