Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises – of varying levels of difficulty – are provided to help the reader master the techniques and reinforce their grasp of the material.

A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters.

The book is written primarily for:

  • advanced undergraduate and graduate students in mathematics and computer science
  • researchers in mathematics and computer science

It will also be of interest to those working in the applied sciences: biology, chemistry, theoretical physics, electrical engineering.