Combinatorics and Graph Theory (Undergraduate Texts in Mathematics) [Hardcover]

John M. Harris (Author), Jeffry L. Hirst (Author), Michael J. Mossinghoff (Author)

Book Description

Publication Date: July 19, 2000 | ISBN-10: 0387987363 | ISBN-13: 978-0387987361 | Edition: 1

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, Pólya theory, the stable marriage problem, and several important classes of numbers. Chapter 3 presents infinite pigeonhole principles, König's lemma, and Ramsey's theorem, and discusses their connections to axiomatic set theory. The text is written in an enthusiastic and lively style. It 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.

Editorial Reviews

Review

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 text written with them in mind. Each of the three chapters concludes with several paragraphs describing an excellent selection of more advanced texts or papers to consider for further study"

From the Back Cover

This book covers a wide variety of topics in combinatorics and graph theory. It 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 second edition includes many new topics and features: • New sections in graph theory on distance, Eulerian trails, and Hamiltonian paths. • New material on partitions, multinomial coefficients, and the pigeonhole principle. • Expanded coverage of Pólya Theory to include de Bruijn’s method for counting arrangements when a second symmetry group acts on the set of allowed colors. • Topics in combinatorial geometry, including Erdos and Szekeres’ development of Ramsey Theory in a problem about convex polygons determined by sets of points. • Expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable. • Numerous new exercises throughout the book. About the First Edition: ". . . this is what a textbook should be! The book is comprehensive without being overwhelming, the proofs are elegant, clear and short, and the examples are well picked." — Ioana Mihaila, MAA Reviews --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 304 pages
• Publisher: Springer; 1 edition (July 19, 2000)
• Language: English
• ISBN-10: 0387987363
• ISBN-13: 978-0387987361
• Product Dimensions: 9.2 x 6.4 x 0.9 inches
• Shipping Weight: 1.1 pounds
• Average Customer Review: 4.4 out of 5 stars  See all reviews (12 customer reviews)
• Amazon Best Sellers Rank: #1,521,757 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

19 of 20 people found the following review helpful:

5.0 out of 5 stars Perfect book for self teaching, March 3, 2007

By 

Richard A. Robertson (Jacksonville, FL United States) - See all my reviews
(REAL NAME)   

This review is from: Combinatorics and Graph Theory (Undergraduate Texts in Mathematics) (Hardcover)

I am a math student with Indiana University working out of this book for independent study credit. When my adviser and I sat down to discuss books, we sifted through 10 to 12 books, and it was clear from the start that this book was the best. And I haven't changed my mind since. The book is clear, concise, and easy to read. Excellent for anyone who is teaching themselves, which of course means it's great for a full course with actual instructors.

9 of 9 people found the following review helpful:

5.0 out of 5 stars A truly elegant introduction to combinatorics, May 23, 2007

By 

Peter M. Magyar "peter-the-math-geek" (East Lansing, MI United States) - See all my reviews
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This review is from: Combinatorics and Graph Theory (Undergraduate Texts in Mathematics) (Hardcover)

Unlike its competitors, this book states simple concepts simply. It gives an excellent selection of the most important techniques and examples, without endlessly repeated "real-world" applications. In 80 pages, it covers the most interesting topics in graph theory, including: Cayley's tree-counting theorem, vertex coloring (with proof of the 5-Color Theorem), Hall matching theorem, Ramsey numbers, and stable marriage. Another 80 pages contains the main concepts of enumeration: elementary combinations (poker hands), inclusion-exclusion, generating functions for Fibonacci and Catalan numbers, Polya counting of symmetry classes, Stirling numbers. There is final section on infinite sets and graphs.

The book covers quite as much as similar ones of twice the length. Finally, a textbook which is not afraid to be brief!

20 of 24 people found the following review helpful:

5.0 out of 5 stars What an introductory book on combinatorics should be, June 3, 2003

By 

Hasnor Lot (Minneapolis) - See all my reviews

This review is from: Combinatorics and Graph Theory (Undergraduate Texts in Mathematics) (Hardcover)

Little did I expect of a book that has seemingly not garnered that much attention among professors and students (at least the lack of reviews in Amazon.com might serve as a confirming instance of that speculation), but come exam time, the book proved that such prejudice is outright foolish.

The authors must really love both the field and writing about it, for their overflowing exuberance readily transfers to the pages. Pictures and humor are never a scarcity here: the authors took no shame providing both; a curious but pleasurably fresh anomaly in the often dry and coldly serious world that is mathematics writing.