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A note on groups of colour preserving automorphisms

✍ Scribed by Ulrike Baumann; Ute Holthaus

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 233 KB
Volume: 284
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200910089

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✦ Synopsis

Abstract

A perfect edge colouring of a graph is defined by the property that all colour matchings are perfect matchings. Every edge‐coloured graph determines a group of graph automorphisms which preserve the colours of the edges. If the graph is connected, then this group of colour preserving automorphisms is a semiregular permutation group. The question which semiregular permutation groups with exactly one orbit or with an even number k of orbits arise as groups of colour preserving automorphisms of graphs with perfect edge colourings has been answered in 1,2. The present paper deals with the problem for semiregular permutation groups with an odd number of orbits.

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