Graph theory. 2nd ed.

*(English)*Zbl 0945.05002
Graduate Texts in Mathematics. 173. Berlin: Springer. xiv, 313 p. (2000).

This book is a concise introduction to modern graph theory covering all its topics in the following chapters: The basics. Matching. Connectivity. Planar graphs. Colouring. Flows. Substructures in dense graphs. Substructures in sparse graphs. Ramsey theory for graphs. Hamilton cycles. Random graphs. Minors, trees, and well-quasi-ordering. The symbols and terms defined are listed in the margin; these margins also contain reference numbers of those results that are used in the proofs.

This second edition extends the first in two major changes. The last chapter now gives a complete proof of one of the major results of the Robertson-Seymour theory. The second major change is the addition of a complete set of hints for the exercises, 250 in all. Apart from these two changes, there are a few additions. Among others a new proof of Menger’s theorem.

The book has every chance of becoming a standard textbook of contemporary graph theory.

This second edition extends the first in two major changes. The last chapter now gives a complete proof of one of the major results of the Robertson-Seymour theory. The second major change is the addition of a complete set of hints for the exercises, 250 in all. Apart from these two changes, there are a few additions. Among others a new proof of Menger’s theorem.

The book has every chance of becoming a standard textbook of contemporary graph theory.

Reviewer: J.Fiamčik (Prešov)