This is a well-conceived and well-written book. The authors decided to write an unusally long but very welcome introductory part. This part takes up the first five chapters, and it makes the book self-contained, since it covers basic notions from the definitions of graph and degrees to trees and connectivity, to Eulerian and Hamiltonian graphs, matchings, and planar graphs. Chromatic graph theory comes only after that, in the remaining nine chapters.

These chapters (6–14) are exclusively about graph colorings, roughly equally divided between vertex colorings and edge colorings. Beside the classic topics, such as Ramsey theory, the Turán theorem, and the chromatic number of a graph, we can also learn about less well-known notions, such as the Grundy number of a graph, Rainbow Ramsey numbers, and Radio colorings. The balance between old and new is well struck.

The fact that more than one-third of the book is about graphs in general makes the book suitable not just for a course in chromatic graph theory, but for a course in graph theory in general. This is a major feat — the authors managed to write about a special topic without losing the chance for a wide audience. Whether the course taught from the book is advanced undergraduate or first-year graduate will depend on the school.

The book is written in a reader-friendly style, and there is a sufficient number of exercises at the end of each chapter. My only critical remark is that none of these exercises come with solutions, or even hints. This may not bother professors teaching a course from the book, but will surely upset students, especially those learning on their own, or taking a reading course.

Miklós Bóna is Associate Professor of Mathematics at the University of Florida.