Homogeneous factorisations of complete multipartite graphs

Michael Giudici; Cai-Heng Li; P Potocnik; Cheryl Praeger

doi:10.1016/j.disc.2005.09.034

Homogeneous factorisations of complete multipartite graphs

Michael Giudici, Cai-Heng Li, P Potocnik, Cheryl Praeger

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8 Citations (Scopus)

Abstract

A homogeneous factorisation of a graph is a partition of its arc set such that there exist vertex transitive subgroups M < G <= Aut(Gamma) with M fixing each part of the partition setwise and G preserving the partition and transitively permuting the parts. In this paper we study homogeneous factorisations of complete multipartite graphs such that M acts regularly on vertices. We provide a necessary and sufficient condition for the existence of such factorisations and produce many interesting examples. In particular we give a complete determination of the parameters for which homogeneous factorisations exist with M cyclic. (c) 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	415-431
Journal	Discrete Mathematics
Volume	307
Issue number	3-5
DOIs	https://doi.org/10.1016/j.disc.2005.09.034
Publication status	Published - 2007

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10.1016/j.disc.2005.09.034

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abstract = "A homogeneous factorisation of a graph is a partition of its arc set such that there exist vertex transitive subgroups M < G <= Aut(Gamma) with M fixing each part of the partition setwise and G preserving the partition and transitively permuting the parts. In this paper we study homogeneous factorisations of complete multipartite graphs such that M acts regularly on vertices. We provide a necessary and sufficient condition for the existence of such factorisations and produce many interesting examples. In particular we give a complete determination of the parameters for which homogeneous factorisations exist with M cyclic. (c) 2006 Elsevier B.V. All rights reserved.",

author = "Michael Giudici and Cai-Heng Li and P Potocnik and Cheryl Praeger",

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AU - Giudici, Michael

AU - Li, Cai-Heng

AU - Potocnik, P

AU - Praeger, Cheryl

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N2 - A homogeneous factorisation of a graph is a partition of its arc set such that there exist vertex transitive subgroups M < G <= Aut(Gamma) with M fixing each part of the partition setwise and G preserving the partition and transitively permuting the parts. In this paper we study homogeneous factorisations of complete multipartite graphs such that M acts regularly on vertices. We provide a necessary and sufficient condition for the existence of such factorisations and produce many interesting examples. In particular we give a complete determination of the parameters for which homogeneous factorisations exist with M cyclic. (c) 2006 Elsevier B.V. All rights reserved.

AB - A homogeneous factorisation of a graph is a partition of its arc set such that there exist vertex transitive subgroups M < G <= Aut(Gamma) with M fixing each part of the partition setwise and G preserving the partition and transitively permuting the parts. In this paper we study homogeneous factorisations of complete multipartite graphs such that M acts regularly on vertices. We provide a necessary and sufficient condition for the existence of such factorisations and produce many interesting examples. In particular we give a complete determination of the parameters for which homogeneous factorisations exist with M cyclic. (c) 2006 Elsevier B.V. All rights reserved.

U2 - 10.1016/j.disc.2005.09.034

DO - 10.1016/j.disc.2005.09.034

M3 - Article

SN - 0012-365X

VL - 307

SP - 415

EP - 431

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 3-5

ER -

Homogeneous factorisations of complete multipartite graphs

Abstract

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