Extremal Graph Theory

Author: Bela Bollobas
Publisher: Courier Corporation
ISBN: 0486317587
Format: PDF
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The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory. Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find this text a valuable resource in terms of its unusually large collection of results and proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope.

Graph Theory

Author: Ronald Gould
Publisher: Courier Corporation
ISBN: 0486320367
Format: PDF, Docs
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An introductory text in graph theory, this treatment covers primary techniques and includes both algorithmic and theoretical problems. Algorithms are presented with a minimum of advanced data structures and programming details. 1988 edition.

A Seminar on Graph Theory

Author: Frank Harary
Publisher: Courier Dover Publications
ISBN: 0486796841
Format: PDF, Mobi
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Lectures given in F. Harary's seminar course, University College of London, Dept. of Mathematics, 1962-1963.

Pearls in Graph Theory

Author: Nora Hartsfield
Publisher:
ISBN: 9780123285539
Format: PDF
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The Dover edition reprints the 1994 Academic Press edition, which itself was an augmented and revised version of a 1990 work. Harsfield (Western Washington U.) and Ringel (U. of California, Santa Cruz) cover basic graph theory, coloring of graphs, circuits and cycles, extremal problems, counting, la

Computational Discrete Mathematics

Author: Sriram Pemmaraju
Publisher: Cambridge University Press
ISBN: 1107268710
Format: PDF, ePub
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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.

Handbook of Combinatorics

Author: Gerard Meurant
Publisher: Elsevier
ISBN: 0080933351
Format: PDF
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Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.