This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book into three main parts, the authors take readers from the rudiments of chromatic polynomials to more complex topics: the chromatic equivalence classes of graphs and the zeros and inequalities of chromatic polynomials. The early material is well suited to a graduate level course while the latter parts will be an invaluable resource for postgraduate students and researchers in combinatorics and graph theory.

Contents:

• The Number of λ-Colourings and Its Enumerations
• Chromatic Polynomials
• Chromatic Equivalence of Graphs
• Chromaticity of Multi-Partite Graphs
• Chromaticity of Subdivisions of Graphs
• Graphs in Which any Two Colour Classes Induce a Tree
• Graphs in Which All but One Pair of Colour Classes Induce Trees
• Chromaticity of Extremal 3-Colorable Graphs
• Polynomials Related to Chromatic Polynomials
• Real Roots of Chromatic Polynomials
• Integral Roots of Chromatic Polynomials
• Complex Roots of Chromatic Polynomials
• Inequalities on Chromatic Polynomials

“This book is clearly written, well illustrated, and supplied with carefully designed exercises, it takes pleasure in using it as an graduate textbook or for independent study. It leads the reader to the frontiers of present research in the theory of chromatic polynomials and offers insight into some exciting development.”