Combinatorics and graph theory

By:

Harris, John M

Contributor(s):

Material type: Text

9780387987361
0387987363

Subject(s):

DDC classification:

511.64 HAR

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.

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 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."--Jacket.

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Reference Books	Main Library Reference	Reference	511.64 HAR (Browse shelf(Opens below))	Available		011013

Total holds: 0

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Previous	511.6 ADH Aspects of combinatorics and combinatorial number theory	511.6 PEM Computational discrete mathematics : combinatorics and graph theory with Mathematica	511.6 TUC Applied Combinatorics	511.64 HAR Combinatorics and graph theory	511.64 KRI Combinatorics: Theory and Applications	511.8 ALG Algorithms in Bioinformatics	511.8 BRA Fundamentals of algorithmics	Next

Includes index

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.

"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."--Jacket.

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