The title is certainly truthful. The author does cover every subject that can be reasonably included in an undergraduate combinatorics course that has a serious graph theory component (but is not simply a course in graph theory). We find chapters on trees, structure and degrees, vertex coloring, planarity, Hamiltonian graphs, and matchings, as well as a section on Ramsey numbers, and one on list colorings. As the title promises, the treatment is very elementary, the proofs are short and clear, and the theorems are usually broken up into parts so that no individual theorem is too complicated. There are plenty of exercises, though none of them come with solutions, or even, answers.

This reviewer believes that one major audience for the book will be instructors who will use some of the exercises for their class. Adoption for the book as a textbook for a course is trickier – in a general combinatorics course, you want more than just graph theory, and in a graph theory course, some instructors might want something less fundamental. The book can also be used as a reference material by students who simply want to look up a few facts and their reader-friendly proofs.

My only constructive criticism is that the misspelling (by omiting diacritical marks) of the names of very famous mathematicians from non-English speaking countries, such as Erdős, Lovász, Turán, Prüfer, Hajós, and Kőnig, as well as the city of Königsberg, is an unnecessary distraction that would have been very easy to avoid. Here is hoping that this will be fixed in a second printing.

Miklós Bóna (bona@ufl.edu) is a Professor and Distinguished Teaching Scholar at the University of Florida, and the author and editor of several books. His main research interest is Enumerative Combinatorics.