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Combinatorics and graph theory

Author: John M Harris; Jeffry L Hirst; Michael J Mossinghoff
Publisher: New York : Springer, ©2000.
Series: Undergraduate texts in mathematics.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA. Chapter 1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey theory. Chapter 2 studies combinatorics, including the principle of inclusion and exclusion, generating functions, recurrence relations, Polya theory, the stable marriage problem, and several  Read more...
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: John M Harris; Jeffry L Hirst; Michael J Mossinghoff
ISBN: 0387987363 9780387987361
OCLC Number: 42476778
Description: xiii, 225 p. : ill. ; 25 cm.
Contents: 1. Graph theory --
1.1 Introductory concepts --
1.2 Trees --
1.3 Planarity --
1.4 Colorings --
1.5 Matchings --
1.6 Ramsey theory --
1.7 References --
2. Combinatorics --
2.1 Three basic problems --
2.2 Binomial coefficients --
2.3 The principle of inclusion and exclusion --
2.4 Generating functions --
2.5 Pólya's theory of counting --
2.6 More numbers --
2.7 Stable marriage --
2.8 References --
3. Infinite combinatorics and graphs --
3.1 Pigeons and trees --
3.2 Ramsey revisited --
3.3 ZFC --
3.4 The return of der König --
3.5 Ordinals, cardinals, and many pigeons --
3.6 Incompleteness and cardinals --
3.7 Weakly compact cardinals --
3.8 Finite combinatorics with infinite consequences --
3.9 Points of departure --
3.10 References.
Series Title: Undergraduate texts in mathematics.
Responsibility: John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff.
More information:

Abstract:

Evolved from several courses in combinatorics and graph theory. This book contains chapters that: focus on finite graph theory; studies combinatorics; presents infinite pigeonhole principles,  Read more...

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From the reviews: SIAM REVIEW "The narrative and proofs are well written, and the authors are given to frequent uses of humor. Students should find this book as easy to read as any other good-quality Read more...

 
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schema:description"1. Graph theory -- 1.1 Introductory concepts -- 1.2 Trees -- 1.3 Planarity -- 1.4 Colorings -- 1.5 Matchings -- 1.6 Ramsey theory -- 1.7 References -- 2. Combinatorics -- 2.1 Three basic problems -- 2.2 Binomial coefficients -- 2.3 The principle of inclusion and exclusion -- 2.4 Generating functions -- 2.5 Pólya's theory of counting -- 2.6 More numbers -- 2.7 Stable marriage -- 2.8 References -- 3. Infinite combinatorics and graphs -- 3.1 Pigeons and trees -- 3.2 Ramsey revisited -- 3.3 ZFC -- 3.4 The return of der König -- 3.5 Ordinals, cardinals, and many pigeons -- 3.6 Incompleteness and cardinals -- 3.7 Weakly compact cardinals -- 3.8 Finite combinatorics with infinite consequences -- 3.9 Points of departure -- 3.10 References."@en
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schema:reviewBody""This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA. Chapter 1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey theory. Chapter 2 studies combinatorics, including the principle of inclusion and exclusion, generating functions, recurrence relations, Polya theory, the stable marriage problem, and several important classes of numbers. Chapter 3 presents infinite pigeonhole principles, Konig's lemma, and Ramsey's theorem, and discusses their connections to axiomatic set theory." "The text includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The text is primarily directed toward upper-division undergraduate students, but lower-division undergraduates with a penchant for proof and graduate students seeking an introduction to these subjects will also find much of interest."--BOOK JACKET."
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