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Isomorphic factorisations V: Directed graphs

Part of: Graph theory

Published online by Cambridge University Press:  26 February 2010

Frank Harary ,
Robert W. Robinson  and
Nicholas C. Wormald
Frank Harary
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109, U.S.A.
Robert W. Robinson
Affiliation:
Department of Mathematics, University of Newcastle, New South Wales, 2308, Australia.
Nicholas C. Wormald
Affiliation:
Department of Mathematics, University of Newcastle, New South Wales, 2308, Australia.
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Abstract

An isomorphic factorisation of a digraph D is a partition of its arcs into mutually isomorphic subgraphs. If such a factorisation of D into exactly t parts exists, then t must divide the number of arcs in D. This is called the divisibility condition. It is shown conversely that the divisibility condition ensures the existence of an isomorphic factorisation into t parts in the case of any complete digraph. The sufficiency of the divisibility condition is also investigated for complete m-partite digraphs. It is shown to suffice when m = 2 and t is odd, but counterexamples are provided when m = 2 and t is even, and when m = 3 and either t = 2 or t is odd.

MSC classification

Secondary: 05C20: Directed graphs (digraphs), tournaments
Type
Research Article
Information
Mathematika , Volume 25 , Issue 2 , December 1978 , pp. 279 - 285
Copyright
Copyright © University College London 1978

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References

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