Extremal Combinatorics

With Applications in Computer Science

  • Stasys Jukna
Part of the Texts in Theoretical Computer Science. An EATCS Series book series (TTCS)

Table of contents

  1. Front Matter
    Pages I-XXIII
  2. The Classics

    1. Front Matter
      Pages 1-1
    2. Stasys Jukna
      Pages 3-22
    3. Stasys Jukna
      Pages 23-39
    4. Stasys Jukna
      Pages 41-51
    5. Stasys Jukna
      Pages 53-75
    6. Stasys Jukna
      Pages 77-86
  3. Extremal Set Theory

    1. Front Matter
      Pages 87-87
    2. Stasys Jukna
      Pages 89-98
    3. Stasys Jukna
      Pages 99-106
    4. Stasys Jukna
      Pages 107-118
    5. Stasys Jukna
      Pages 119-134
    6. Stasys Jukna
      Pages 135-154
    7. Stasys Jukna
      Pages 155-163
    8. Stasys Jukna
      Pages 165-176
  4. The Linear Algebra Method

    1. Front Matter
      Pages 177-177
    2. Stasys Jukna
      Pages 179-196
    3. Stasys Jukna
      Pages 197-212
    4. Stasys Jukna
      Pages 213-222
    5. Stasys Jukna
      Pages 223-236

About this book

Introduction

This book is a concise, self-contained, up-to-date introduction to extremal combinatorics for nonspecialists. There is a strong emphasis on theorems with particularly elegant and informative proofs, they may be called gems of the theory. The author presents a wide spectrum of the most powerful combinatorial tools together with impressive applications in computer science: methods of extremal set theory, the linear algebra method, the probabilistic method, and fragments of Ramsey theory. No special knowledge in combinatorics or computer science is assumed – the text is self-contained and the proofs can be enjoyed by undergraduate students in mathematics and computer science. Over 300 exercises of varying difficulty, and hints to their solution, complete the text.

This second edition has been extended with substantial new material, and has been revised and updated throughout. It offers three new chapters on expander graphs and eigenvalues, the polynomial method and error-correcting codes. Most of the remaining chapters also include new material, such as the Kruskal—Katona theorem on shadows, the Lovász—Stein theorem on coverings, large cliques in dense graphs without induced 4-cycles, a new lower bounds argument for monotone formulas, Dvir's solution of the finite field Kakeya conjecture, Moser's algorithmic version of the Lovász Local Lemma, Schöning's algorithm for 3-SAT, the Szemerédi—Trotter theorem on the number of point-line incidences, surprising applications of expander graphs in extremal number theory, and some other new results.

Keywords

Combinatorics Discrete Probability Error-Correcting Codes Extremal Combinatorics Extremal Set Theory Linear Algebra Linear Algebra Method Polynomial Method Probabilistic Method Ramsey Theory

Authors and affiliations

  • Stasys Jukna
    • 1
  1. 1.Institut für InformatikGoethe Universität FrankfurtFrankfurt am MainGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-17364-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-642-17363-9
  • Online ISBN 978-3-642-17364-6
  • Series Print ISSN 1862-4499
  • About this book