Overview

Over the past decade, many major advances have been made in the field of graph coloring via the probabilistic method. This monograph, by two of the best on the topic, provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality.

Full Product Details

Author:   Michael Molloy ,  Bruce Reed
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 2002
Volume:   23
ISBN:  

9783642040153

ISBN 10:   3642040152
Pages:   326
Publication Date:   04 December 2002
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1. Colouring Preliminaries.- 2. Probabilistic Preliminaries.- 3. The First Moment Method.- 4. The Lovasz Local Lemma.- 5. The Chernoff Bound.- 6. Hadwiger's Conjecture.- 7. A First Glimpse of Total Colouring.- 8. The Strong Chromatic Number.- 9. Total Colouring Revisited.- 10. Talagrand's Inequality and Colouring Sparse Graphs.- 11. Azuma's Inequality and a Strengthening of Brooks' Theorem.- 12. Graphs with Girth at Least Five.- 13. Triangle-Free Graphs.- 14. The List Colouring Conjecture.- 15. The Structural Decomposition.- 16. ?, ? and ?.- 17. Near Optimal Total Colouring I: Sparse Graphs.- 18. Near Optimal Total Colouring II: General Graphs.- 19. Generalizations of the Local Lemma.- 20. A Closer Look at Talagrand's Inequality.- 21. Finding Fractional Colourings and Large Stable Sets.- 22. Hard-Core Distributions on Matchings.- 23. The Asymptotics of Edge Colouring Multigraphs.- 24. The Method of Conditional Expectations.- 25. Algorithmic Aspects of the Local Lemma.- References.

Reviews

From the reviews of the first edition: The presented book contains many ... chapters, each of which presents a proof technique and apply that for a certain graph coloring problem. ... The book ends with a vast bibliography. We think that this well-written monograph will serve as a main reference on the subject for years to come. (Janos Barat, Acta Scientiarum Mathematicarum, Vol. 69, 2003) The book is a pleasure to read; there is a clear, successful attempt to present the intuition behind the proofs, making even the difficult, recent proofs of important results accessible to potential readers. ... The book is highly recommended to researchers and graduate students in graph theory, combinatorics, and theoretical computer science who wish to have this ability. (Noga Alon, SIAM Review, Vol. 45 (2), 2003) The probabilistic method in graph theory was initiated by Paul Erdoes in 1947 ... . This book is an introduction to this powerful method. ... The book is well-written and brings the researcher to the frontiers of an exciting field. (M.R. Murty, Short Book Reviews, Vol. 23 (1), April, 2003) This monograph provides an accessible and unified treatment of major advances made in graph colouring via the probabilistic method. ... Many exercises and excellent remarks are presented and discussed. Also very useful is the list of up-to-date references for current research. This monograph will be useful both to researchers and graduate students in graph theory, discrete mathematics, theoretical computer science and probability. (Jozef Fiamcik, Zentralblatt MATH, Vol. 987 (12), 2002)

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