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The Petersen Graph
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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.
Title: The Petersen Graph
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 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.
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