Combinatorics and Graph Theory

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Springer Science & Business Media, Sep 19, 2008 - Mathematics - 381 pages
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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.

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This text does exactly as it sets out to do. It introduces material very quickly and precisely with little to no confusion. The author frequently use humor throughout the text which makes the text even more pleasurable to read. Although rather brief the text covers a multitude of information and demands a high level of mathematical maturity. Some questions are not trivial! (For example, one problem asks to proof Hall's Theorem using Tutte's Theorem.) Each question in the text requires some thought and actually enhances one's understanding of the material. Excellent book, first rate for self study. 

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