The Petersen graph has fascinated many graph theorists over the years because of its appearance as a counterexample in many places. Because of its ubiquity, it seemed a natural graph to use as a central theme for a book. As a result of using this graph as our centre piece, much of this book deals with the properties of cubic 3-connected graphs and the ideas that generalize from them.

Incidentally, a biography of Julius Petersen can be found in J.Lützen, G.Sabidussi, B. Toft, Julius Petersen 1839–1910, A Biography, Preprint, Odense University, 1990.

The book has grown out of lecture courses that we have given in various places over a number of years. In all cases the audience were final honours year students, graduate students or research colleagues. Hence we would expect the current volume to be useful for senior students and research workers. Because of this we have included a reasonably large number of Exercises and an extensive set of references.

In citing references we have used the form [A-B 34] for the 1934 paper of the authors Able and Baker and [aB 34] for the 1934 (or perhaps 1834) paper of the single author A. Board. When two authors have the same initials an extra letter has been inserted to distinguish between them so [aB 89] becomes [aaB 89] if there is another author with initials A, B. References for each chapter are at the end of that chapter.

Figures, lemmas, theorems, corollaries, conjectures, etc., are numbered consecutively throughout each section of each chapter.