Topics in Chromatic Graph Theory

A broad survey written by acknowledged international experts in the field.

Lowell W. Beineke (Edited by), Robin J. Wilson (Edited by)

9781107033504, Cambridge University Press

Hardback, published 7 May 2015

386 pages, 65 b/w illus.
24.1 x 16.3 x 2.5 cm, 0.72 kg

Chromatic graph theory is a thriving area that uses various ideas of 'colouring' (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such areas as computer networks, where colouring algorithms form an important feature. While other books cover portions of the material, no other title has such a wide scope as this one, in which acknowledged international experts in the field provide a broad survey of the subject. All fifteen chapters have been carefully edited, with uniform notation and terminology applied throughout. Bjarne Toft (Odense, Denmark), widely recognized for his substantial contributions to the area, acted as academic consultant. The book serves as a valuable reference for researchers and graduate students in graph theory and combinatorics and as a useful introduction to the topic for mathematicians in related fields.

Foreword Bjarne Toft
Preface
Preliminaries Lowell W. Beineke and Robin J. Wilson
1. Colouring graphs on surfaces Bojan Mohar
2. Brooks's theorem Michael Stiebitz and Bjarne Toft
3. Chromatic polynomials Bill Jackson
4. Hadwiger's conjecture Ken-ichi Kawarabayashi
5. Edge-colourings Jessica McDonald
6. List-colourings Michael Stiebitz and Margit Voigt
7. Perfect graphs Nicolas Trotignon
8. Geometric graphs Alexander Soifer
9. Integer flow and orientation Hongjian Lai, Rong Luo and Cun-Quan Zhang
10. Colouring random graphs Ross J. Kang and Colin McDiarmid
11. Hypergraph colouring Csilla Bujtas, Zsolt Tuza and Vitaly Voloshin
12. Chromatic scheduling Dominique de Werra and Alain Hertz
13. Graph colouring algorithms Thore Husfeldt
14. Colouring games Zsolt Tuza and Xuding Zhu
15. Open problems Tommy Jensen and Bjarne Toft
Notes on contributors
Index.

Subject Areas: Combinatorics & graph theory [PBV], Algebra [PBF], Discrete mathematics [PBD], Mathematics [PB]