Author:
Sali Attila,Simonyi Gábor,Tardos Gábor
Abstract
AbstractIn an earlier paper (see Sali and Simonyi Eur. J. Combin. 20, 93–99, 1999) the first two authors have shown that self-complementary graphs can always be oriented in such a way that the union of the oriented version and its isomorphically oriented complement gives a transitive tournament. We investigate the possibilities of generalizing this theorem to decompositions of the complete graph into three or more isomorphic graphs. We find that a complete characterization of when an orientation with similar properties is possible seems elusive. Nevertheless, we give sufficient conditions that generalize the earlier theorem and also imply that decompositions of odd vertex complete graphs to Hamiltonian cycles admit such an orientation. These conditions are further generalized and some necessary conditions are given as well.
Funder
Hungarian Scientific Research Fund
Magyar Tudományos Akadémia
European Research Council
Russian Government Grant
Nemzeti Kutatási, Fejlesztési és Innovaciós Alap
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Geometry and Topology,Algebra and Number Theory
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