- Series: Undergraduate Texts in Mathematics
- Hardcover: 381 pages
- Publisher: Springer; 2nd ed. 2008 edition (September 19, 2008)
- Language: English
- ISBN-10: 0387797106
- ISBN-13: 978-0387797106
- Product Dimensions: 6.1 x 0.9 x 9.2 inches
- Shipping Weight: 1.5 pounds (View shipping rates and policies)
- Average Customer Review: 3.6 out of 5 stars See all reviews (13 customer reviews)
- Amazon Best Sellers Rank: #548,942 in Books (See Top 100 in Books)
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Combinatorics and Graph Theory (Undergraduate Texts in Mathematics) 2nd ed. 2008 Edition
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From the reviews:
"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 reviews of the second edition:
“Any undergraduate work in combinatorics or graph theory, whether a course or independent study, would likely be well served by this textbook … . The authors offer a wide selection of topics, often in more depth than other undergraduate texts, in an engaging and clear style. … Each chapter concludes with extensive notes on further reading.” (Brian Hopkins, Mathematical Reviews, Issue 2010 b)
“Combinatorics and Graph Theory is a popular pair of topics to choose for an undergraduate course. … The book is written in a reader-friendly style and there are enough exercises. … It is certainly good that someone took the effort to write … in a form that is appropriate for undergraduates. … the book will most often be used for a reading class by a student who already has a background in combinatorics and who wants to learn about the set theoretical aspect of it.” (Miklós Bóna, SIGACT News, Vol. 40 (3), 2009)
“This undergraduate textbook contains three chapters: Graph Theory, Combinatorics and Infinite Combinatorics and Graphs. … There is a short section on References in each chapter introducing briefly other books dealing with the topics covered in the respective chapter. A full list of 293 references, about 550 exercises and an index with 13 pages are also provided.” (Dalibor Froncek, Zentralblatt MATH, Vol. 1170, 2009)
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
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Top Customer Reviews
My negative experience was especially compounded by my professor's ineptitude at Graph Theory, but trying to set that bias aside I really wish this book was turned into a full textbook that worked on fixing its many flaws. My biggest peeve is that it is very hard to use as a reference since the authors do not even glossary concepts. Most are italicized (which is impossible to spot in this font), but still others are just not.
Overall, perhaps a future version will be worth using in the classroom or for reference, but this version is not able to reach those standards.
The problem I had with discrete math textbooks were they treated graph theory as some sort of sideshow attraction to fill the book.
And the point was to show off neat examples, and not really provide a solid foundation in graph theory.
The authors go beyond Eulers bridges problem and color counting. The theorems are presented with the proofs, and they have just enough examples to instruct. Could they add a bunch more examples and flashy sidebars? sure. However, the authors provide enough examples when needed without fluff, but more important they provide solid coverage on graph theory.
The only real negative is the writing style is not as great as one would hope.
Combinatorics coverage has some interesting depth beyond the standard textbooks. The stable marriage problem alone is examined to n-degrees of depth with variations on solutions.
Polyas theory of counting is extensively presented as well. ( Yes Euler gets his number theory coverage as well ).
Overall there are flaws with the book, but nothing earth shattering. The authors did a great job of covering the topics beyond the basics, and leveraged examples to illustrate variations which really made this book shine.
This book's explanations dealing with poker hands did what Tucker's and Grimaldi's books left me hanging on. Treatment on the binomial theorem and its related applications was also very thorough and at an acceptable level. The beauty of this book however is that the exercises rapidly increase in punch, and I still return to it from time to time to tease out new relationships.
It's introduction to graph theory is also very stellar... and it decides to introduce it before the combinatorial arguments, which if I'd had a little stronger comp sci background before taking the class, I would have found a much more gradual introduction to the general theories.
I'm still raising in mathematical ability, and I plan on tackling this book when I've gotten a little more maturity under my belt.
Excellent book. Hands down.