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.
| ISBN: | 9783540421399 |
| Publication date: | 20th November 2001 |
| Author: | Michael S Molloy, Bruce A Reed |
| Publisher: | Springer an imprint of Springer Berlin Heidelberg |
| Format: | Hardback |
| Pagination: | 326 pages |
| Series: | Algorithms and Combinatorics |
| Genres: |
Probability and statistics Stochastics Algorithms and data structures Mathematical theory of computation Discrete mathematics |
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.
Graph Colouring and the Probabilistic Method features in the following genres: Probability and statistics, Stochastics, Algorithms and data structures, Mathematical theory of computation, Discrete mathematics
Hardback. Not Available.
Graph Colouring and the Probabilistic Method was written by Michael S Molloy, Bruce A Reed and published by Springer an imprint of Springer Berlin Heidelberg
Graph Colouring and the Probabilistic Method has 326 pages
Yes it is part of Algorithms and Combinatorics series