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© 2000

Combinatorics and Graph Theory

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
    Pages 1-84
  3. John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
    Pages 85-159
  4. John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
    Pages 161-210
  5. Back Matter
    Pages 211-228

About this book

Introduction

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.

Keywords

Combinatorics Matching Pigeonhole principle Polya Ramsey theory graph theory

Authors and affiliations

  1. 1.Department of MathematicsFurman UniversityGreenvilleUSA
  2. 2.Department of MathematicsAppalachian State UniversityBooneUSA
  3. 3.Department of MathematicsUCLALos AngelesUSA

Bibliographic information

  • Book Title Combinatorics and Graph Theory
  • Authors John M. Harris
    Jeffry L. Hirst
    Michael J. Mossinghoff
  • Series Title Undergraduate Texts in Mathematics
  • DOI https://doi.org/10.1007/978-1-4757-4803-1
  • Copyright Information Springer-Verlag New York 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-98736-1
  • Softcover ISBN 978-1-4757-4805-5
  • eBook ISBN 978-1-4757-4803-1
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages XIII, 228
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Topics Combinatorics
  • Buy this book on publisher's site

Reviews

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"