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The Strange Logic of Random Graphs

  • Joel Spencer

Part of the Algorithms and Combinatorics book series (AC, volume 22)

Table of contents

  1. Front Matter
    Pages I-X
  2. Beginnings

    1. Front Matter
      Pages 1-1
    2. Joel Spencer
      Pages 3-12
    3. Joel Spencer
      Pages 13-21
    4. Joel Spencer
      Pages 23-45
  3. Random Graphs

    1. Front Matter
      Pages 47-47
    2. Joel Spencer
      Pages 49-67
    3. Joel Spencer
      Pages 69-77
    4. Joel Spencer
      Pages 79-86
    5. Joel Spencer
      Pages 87-91
    6. Joel Spencer
      Pages 93-102
    7. Joel Spencer
      Pages 103-118
  4. Extras

    1. Front Matter
      Pages 119-119
    2. Joel Spencer
      Pages 121-129
    3. Joel Spencer
      Pages 131-144
    4. Joel Spencer
      Pages 145-151
    5. Joel Spencer
      Pages 153-163
  5. Back Matter
    Pages 165-168

About this book

Introduction

The study of random graphs was begun by Paul Erdos and Alfred Renyi in the 1960s and now has a comprehensive literature. A compelling element has been the threshold function, a short range in which events rapidly move from almost certainly false to almost certainly true. This book now joins the study of random graphs (and other random discrete objects) with mathematical logic. The possible threshold phenomena are studied for all statements expressible in a given language. Often there is a zero-one law, that every statement holds with probability near zero or near one. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.
The book will be of interest to graduate students and researchers in discrete mathematics.

Keywords

Graph combinatorics graph theory logic mathematical logic probability random graphs

Authors and affiliations

  • Joel Spencer
    • 1
  1. 1.Courant InstituteNew York UniversityNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04538-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07499-8
  • Online ISBN 978-3-662-04538-1
  • Series Print ISSN 0937-5511
  • Buy this book on publisher's site