The Petersen Graph (Australian Mathematical Society Lecture Series)
By D. A. Holton, J. Sheehan
* Publisher: Cambridge University Press
* Number Of Pages: 363
* Publication Date: 1993-06-25
* ISBN-10 / ASIN: 0521435943
* ISBN-13 / EAN: 9780521435949
* Binding: Paperback
Product Description:
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 colorability (including snarks), factors, flows, projective geometry, cages, hypohamiltonian graphs, and "symmetry" properties such as distance transitivity. The final chapter contains a potpourri of other topics in which the Petersen graph has played its part.
Summary: A fascinating survey of topics in graph theory
Rating: 5
The Petersen graph is a small graph which shows up amazingly often as a counterexample in graph theory. Holton and Sheehan use it as a starting point to discuss several topics, such as the four-color problem and "snarks", cages, symmetry conditions on graphs, and hypohamiltonian graphs. Graph theory is kind of a hobby of mine, and I find this book an absorbing mishmash of introductory material. It's very accessible, and gives a real sense of a live field, full of conjectures.
The level is probably appropriate for a smart math undergrad. A little knowledge of graphs would be good, and you should know what groups are, and be able to read a proof. The presentation is often a bit sloppy (I had to rewrite some of the proofs to understand them). But still, I definitely want this in my library.
http://ifile.it/2kpy8h3/holton_sheehan.djvu
