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Excluding Minors in Cubic Graphs

Published online by Cambridge University Press:  12 September 2008

K. Kilakos  and
B. Shepherd
K. Kilakos
Affiliation:
Centre for Discrete and Applicable Mathematics, London School of Economics, London, UK
B. Shepherd
Affiliation:
Centre for Discrete and Applicable Mathematics, London School of Economics, London, UK
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Abstract

Let P10\e be the graph obtained by deleting an edge from the Petersen graph. We give a decomposition theorem for cubic graphs with no minor isomorphic to P10\e. The decomposition is used to show that graphs in this class are 3-edge-colourable. We also consider an application to a conjecture due to Grötzsch which states that a planar graph is 3-edge-colourable if and only if it is fractionally 3-edge-colourable.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 1 , March 1996 , pp. 57 - 78
Copyright
Copyright © Cambridge University Press 1996

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