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Transversals in permutation groups and factorisations of complete graphs

Published online by Cambridge University Press:  17 April 2009

Gil Kaplan  and
Arieh Lev
Gil Kaplan
Affiliation:
Department of Computer Sciences, The Academic College of Tel-Aviv-Yaffo, 4 Antokolsky st., Tel-Aviv, Israel64044
Arieh Lev
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sacker Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, Israel64044
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Abstract

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Let G be a transitive permutation group acting on a finite set of order n. We discuss certain types of transversals for a point stabiliser A in G: free transversals and global transversals. We give sufficient conditions for the existence of such transversals, and show the connection between these transversals and combinatorial problems of decomposing the complete directed graph into edge disjoint cycles. In particular, we classify all the inner-transitive Oberwolfach factorisations of the complete directed graph. We mention also a connection to Frobenius theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 277 - 288
Copyright
Copyright © Australian Mathematical Society 2002

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