Graph Colouring and the Probabilistic Method

by Michael Molloy, Bruce Reed

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 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.

Genres: Mathematics

340 pages, Hardcover

First published December 6, 2001

About the author

As a counterpart to his career as a writer of children's books, Michael Molloy is a regular contributor to the Guardian newspaper. He lives in London, England, with his wife, Sandy, their three daughters, Jane, Kate, and Alexandra, and their two dogs, Fred and Daisy.