The Petersen Graph [Paperback]

The authors examine various areas of graph theory, using the prominent role of the Petersen graph as a unifying feature.The Petersen graph occupies an important position in modern graph theory because it often appears as a counter-example to important conjectures. The authors examine those areas in this text, using the prominent role of the Petersen graph as a unifying feature.The Petersen graph occupies an important position in modern graph theory because it often appears as a counter-example to important conjectures. The authors examine those areas in this text, using the prominent role of the Petersen graph as a unifying feature.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.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.