Graph colouring and the probabilistic method图着色与概率方法

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　　分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者： Michael Molloy等著

出版社：湖南文艺出版社

出版时间： 2001-10-1字数：版次： 1页数： 326印刷时间： 2001/10/01开本： 16开印次： 1纸张：胶版纸I S B N ： 9783540421399包装：精装内容简介

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.

Part I Preliminaries

1 Colouring Preliminaries

2 Probabilistic Preliminaries

Part II Basic Probabilistic Tools

3 The First Moment Method

4 The Lovasz Local Lemma

5 The Chernoff Bound

Part III Vertex Partitions

6 Hadwiger's Conjecture

7 A First Glimpse of Total Colouring

8 The Strong Chromatic Number

9 Total Colouring Revisited

Part IV A Naive Colouring Procedure

10 Talagrand's Inequality and Colouring Sparse Graphs

11 Azuma's Inequality and a Strengthening of Brooks' Theorem

Part V An Iterative Approach

12 Graphs with Girth at Least Five

13 Triangle-Free Graphs

14 The List Colouring Conjecture

Part VI A Structural Decomposition

15 The Structural Decomposition

16 [omega], [Delta] and [chi]

17 Near Optimal Total Colouring I: Sparse Graphs

18 Near Optimal Total Colouring II: General Graphs

Part VII Sharpening our Tools

19 Generalizations of the Local Lemma

20 A Closer Look at Talagrand's Inequality

Part VIII Colour Assignment via Fractional Colouring

21 Finding Fractional Colourings and Large Stable Sets

22 Hard-Core Distributions on Matchings

23 The Asymptotics of Edge Colouring Multigraphs

Part IX Algorithmic Aspects

24 The Method of Conditional Expectations

25 Algorithmic Aspects of the Local Lemma

References

Index