Combinatorics and Graph Theory

1. Front Matter

   Pages i-xiii

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2. Graph Theory

   • John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff

   Pages 1-84

3. Combinatorics

   • John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff

   Pages 85-159

4. Infinite Combinatorics and Graphs

   • John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff

   Pages 161-210

5. Back Matter

   Pages 211-228

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Three things should be considered: problems, theorems, and applications. - Gottfried Wilhelm Leibniz, Dissertatio de Arte Combinatoria, 1666 This book grew out of several courses in combinatorics and graph theory given at Appalachian State University and UCLA in recent years. A one-semester course for juniors at Appalachian State University focusing on graph theory covered most of Chapter 1 and the first part of Chapter 2. A one-quarter course at UCLA on combinatorics for undergraduates concentrated on the topics in Chapter 2 and included some parts of Chapter I. Another semester course at Appalachian State for advanced undergraduates and beginning graduate students covered most of the topics from all three chapters. There are rather few prerequisites for this text. We assume some familiarity with basic proof techniques, like induction. A few topics in Chapter 1 assume some prior exposure to elementary linear algebra. Chapter 2 assumes some familiarity with sequences and series, especially Maclaurin series, at the level typically covered in a first-year calculus course. The text requires no prior experience with more advanced subjects, such as group theory.

• Combinatorics
• Matching
• Pigeonhole principle
• Polya
• Ramsey theory
• graph theory

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"

• Department of Mathematics, Furman University, Greenville, USA

  John M. Harris

• Department of Mathematics, Appalachian State University, Boone, USA

  Jeffry L. Hirst

• Department of Mathematics, UCLA, Los Angeles, USA

  Michael J. Mossinghoff

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