The Petersen Graph

The authors examine various areas of graph theory, using the prominent role of the Petersen graph as a unifying feature.

D. A. Holton (Author), J. Sheehan (Author)

9780521435949, Cambridge University Press

Paperback, published 22 April 1993

364 pages, 46 b/w illus.
22.6 x 15 x 2 cm, 0.507 kg

The Petersen graph occupies an important position in the development of several areas of modern graph theory because it often appears as a counter-example to important conjectures. In this account, the authors examine those areas, using the prominent role of the Petersen graph as a unifying feature. Topics covered include: vertex and edge colourability (including snarks), factors, flows, projective geometry, cages, hypohamiltonian graphs, and 'symmetry' properties such as distance transitivity. The final chapter contains a pot-pourri of other topics in which the Petersen graph has played its part. Undergraduate students will be able to profit from reading this book as the prerequisites are few; thus it could be used for a second course in graph theory. On the other hand, the authors have also included a number of unsolved problems as well as topics of recent study. Thus it will also be useful as a reference for graph theorists.

1. The Petersen graph
2. The four colour problem
3. Snarks
4. Factors
5. Beyond the four colour theorem
6. Cages
7. Hypohamiltonian graphs
8. Symmetry
9. The Petersen graph in diversity
Index.

Subject Areas: Combinatorics & graph theory [PBV]