Chromatic graph theory. (English) Zbl 1169.05001

Chartrand, Gary; Zhang, Ping

Discrete Mathematics and Its Applications. Boca Raton, FL: Chapman & Hall/CRC (ISBN 978-1-58488-800-0/hbk). xiii, 483 p. (2009).

The book provides a course in graph theory with emphasis on graph colourings. The book is written in student-friendly style with carefully explained proofs and examples and contains many exercises of varying difficulty. This self-contained book first presents an introduction to graph theory. The main part of the text covers various modern approaches of graph colouring starting with vertex colourings and bounds for the chromatic number, vertex colourings of graphs embedded on surfaces, and a variety of restricted vertex colourings. The authors also describe edge colourings, monochromatic and rainbow edge colourings, complete vertex colourings, several distinguishing vertex and edge colourings, and many distance-related vertex colourings.
The book is intended for standard courses in graph theory, reading courses and seminars on graph colourings, and as a reference book for individuals interested in graphs colourings.

Reviewer: Gabriel Semanišin (Košice)

MSC:

05-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics
05Cxx	Graph theory
05C15	Coloring of graphs and hypergraphs

Keywords:

graph; proper colouring; generalised colouring; list colouring; distinguished colouring