Homogeneous factorisations of graphs and digraphs

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Abstract

A homogeneous factorisation (M, G, Gamma, P) is a partition P of the arc set of a digraph Gamma such that there exist vertex-transitive groups M < G < Aut(Gamma) such that M fixes each pan of P setwise while G acts transitively on P. Homogeneous factorisations of complete graphs have previously been studied by the second and fourth authors, and are a generalisation of vertex-transitive self-complementary digraphs. In this paper we initiate the study of homogeneous factorisations of arbitrary graphs and digraphs. We give a generic group theoretic construction and show that all homogeneous factorisations can be constructed in this way. We also show that the important homogeneous factorisations to study are those where G acts transitively on the set of arcs of Gamma, m is a normal subgroup of G and G/M is a cyclic group of prime order. (c) 2004 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)11-37
JournalEuropean Journal of Combinatorics
Volume27
Issue number1
DOIs
Publication statusPublished - 2006

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