Graph Colouring and the Probabilistic Method

  • Michael Molloy
  • Bruce Reed

Part of the Algorithms and Combinatorics book series (AC, volume 23)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Michael Molloy, Bruce Reed
      Pages 3-14
    3. Michael Molloy, Bruce Reed
      Pages 15-24
  3. Basic Probabilistic Tools

    1. Front Matter
      Pages 25-25
    2. Michael Molloy, Bruce Reed
      Pages 27-37
    3. Michael Molloy, Bruce Reed
      Pages 39-42
    4. Michael Molloy, Bruce Reed
      Pages 43-46
  4. Vertex Partitions

    1. Front Matter
      Pages 47-47
    2. Michael Molloy, Bruce Reed
      Pages 49-53
    3. Michael Molloy, Bruce Reed
      Pages 55-59
    4. Michael Molloy, Bruce Reed
      Pages 61-65
    5. Michael Molloy, Bruce Reed
      Pages 67-75
  5. A Naive Colouring Procedure

    1. Front Matter
      Pages 77-78
    2. Michael Molloy, Bruce Reed
      Pages 79-89
    3. Michael Molloy, Bruce Reed
      Pages 91-103
  6. An Iterative Approach

    1. Front Matter
      Pages 105-105
    2. Michael Molloy, Bruce Reed
      Pages 107-124
    3. Michael Molloy, Bruce Reed
      Pages 125-138
    4. Michael Molloy, Bruce Reed
      Pages 139-153

About this book

Introduction

Over the past decade, many major advances have been made in the field of graph colouring via the probabilistic method. This monograph provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality.
The topics covered include: Kahn's proofs that the Goldberg-Seymour and List Colouring Conjectures hold asymptotically; a proof that for some absolute constant C, every graph of maximum degree Delta has a Delta+C total colouring; Johansson's proof that a triangle free graph has a O(Delta over log Delta) colouring; algorithmic variants of the Local Lemma which permit the efficient construction of many optimal and near-optimal colourings.
This begins with a gentle introduction to the probabilistic method and will be useful to researchers and graduate students in graph theory, discrete mathematics, theoretical computer science and probability.

Keywords

Graph Graph theory Matching Matchings algorithms computer computer science

Authors and affiliations

  • Michael Molloy
    • 1
  • Bruce Reed
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.Université de Paris VI, CNRSParis Cedex 05France
  3. 3.School of Computer ScienceMcGill UniversityMontrealCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-04016-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-04015-3
  • Online ISBN 978-3-642-04016-0
  • Series Print ISSN 0937-5511
  • About this book
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