Combinatorics and Graph Theory

  • John Harris
  • Jeffry L. Hirst
  • Michael Mossinghoff

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

Table of contents

  1. Front Matter
    Pages i-xv
  2. John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
    Pages 1-127
  3. John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
    Pages 129-280
  4. John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
    Pages 281-353
  5. Back Matter
    Pages 355-381

About this book

Introduction

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

Keywords

Addition Combinatorics Counting Graph Graph Theory Hamiltonian path pigeonhole principle

Authors and affiliations

  • John Harris
    • 1
  • Jeffry L. Hirst
    • 2
  • Michael Mossinghoff
    • 3
  1. 1.Dept. MathematicsFurman UniversityGreenvilleU.S.A.
  2. 2.Mathematical SciencesAppalachian State UniversityBooneU.S.A.
  3. 3.Department of MathematicsDavidson CollegeDavidsonU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-79711-3
  • Copyright Information Springer Science+Business Media, LLC 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-79710-6
  • Online ISBN 978-0-387-79711-3
  • Series Print ISSN 0172-6056
  • About this book