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Rank 3 Transitive Decompositions of Complete Multipartite Graphs

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Abstract

A transitive decomposition of a graph is a partition of the edge or arc set giving a set of subgraphs which are preserved and permuted transitively by a group of automorphisms of the graph. This paper deals with transitive decompositions of complete multipartite graphs preserved by an imprimitive rank 3 permutation group. We obtain a near-complete classification of these when the group in question has an almost simple component.

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Perth, 6009, Western Australia

    Geoffrey Pearce & Cheryl E. Praeger

Authors
  1. Geoffrey Pearce
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  2. Cheryl E. Praeger
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Correspondence to Geoffrey Pearce.

Additional information

G. Pearce was supported by an Australian Postgraduate Award and Jean Rogerson Supplementary Scholarship.

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Pearce, G., Praeger, C.E. Rank 3 Transitive Decompositions of Complete Multipartite Graphs. Graphs and Combinatorics 29, 669–680 (2013). https://doi.org/10.1007/s00373-011-1120-4

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  • DOI: https://doi.org/10.1007/s00373-011-1120-4

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