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Graph colouring and the probabilistic method /

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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 co...

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Bibliographic Details
Main Author: Molloy, Michael S.
Corporate Author: SpringerLink (Online service)
Other Authors: Reed, Bruce A.
Format: eBook
Language:English
Published: Berlin ; New York : Springer, [2002]
Series:Algorithms and combinatorics ; 23.
Subjects:
Graph coloring.
Combinatorial analysis.
Probabilities.
Probability Theory and Stochastic Processes.
Theory of Computation.
Math Applications in Computer Science.
Algorithm Analysis and Problem Complexity.
Grafentheorie.
Kleuren.
Kombinatorische Wahrscheinlichkeitstheorie.
Graphfärbung.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • pt. I. Preliminaries. 1. Colouring Preliminaries. 2. Probabilistic Preliminaries
  • pt. II. Basic Probabilistic Tools. 3. The First Moment Method. 4. The Lovasz Local Lemma. 5. The Chernoff Bound
  • pt. III. Vertex Partitions. 6. Hadwiger's Conjecture. 7. A First Glimpse of Total Colouring. 8. The Strong Chromatic Number. 9. Total Colouring Revisited
  • pt. IV. A Naive Colouring Procedure. 10. Talagrand's Inequality and Colouring Sparse Graphs. 11. Azuma's Inequality and a Strengthening of Brooks' Theorem
  • pt. V. An Iterative Approach. 12. Graphs with Girth at Least Five. 13. Triangle-Free Graphs. 14. The List Colouring Conjecture
  • pt. VI. A Structural Decomposition. 15. The Structural Decomposition.