LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	519.2
Title	Graph Colouring and the Probabilistic Method ([EBook] /) / by Michael Molloy, Bruce Reed.
Author	Molloy, Michael
Added Personal Name	Reed, Bruce author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 2002.
Physical Details	XIV, 326 p. : online resource.
Series	Algorithms and Combinatorics 0937-5511 ; ; 23
ISBN	9783642040160
Summary Note	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.:
Contents note	1. Colouring Preliminaries -- 2. Probabilistic Preliminaries -- 3. The First Moment Method -- 4. The Lovász 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-04016-0
Links to Related Works	Subject References: Algorithm Analysis and Problem Complexity . Algorithms . Combinatorics . Computer Science . Computers . Math Applications in Computer Science . Mathematics . Probabilities . Probability theory and stochastic processes . Theory of Computation . Authors: Molloy, Michael . Reed, Bruce . Corporate Authors: SpringerLink (Online service) . Series: Algorithms and Combinatorics . Classification: 519.2 .

Catalogue Display

Graph Colouring and the Probabilistic Method

Reviews