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SOME RESULTS ON THE OBERWOLFACH PROBLEM

Published online by Cambridge University Press:  01 February 2002

A. J. W. HILTON
Affiliation:
Department of Mathematics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX
MATTHEW JOHNSON
Affiliation:
Department of Mathematics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX
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Abstract

The well-known Oberwolfach problem is to show that it is possible to 2-factorize Kn (n odd) or Kn less a 1-factor (n even) into predetermined 2-factors, all isomorphic to each other; a few exceptional cases where it is not possible are known. A completely new technique is introduced that enables it to be shown that there is a solution when each 2-factor consists of k r-cycles and one (nkr)-cycle for all n [ges ] 6kr−1. Solutions are also given (with three exceptions) for all possible values of n when there is one r-cycle, 3 [les ] r [les ] 9, and one (nr)-cycle, or when there are two r-cycles, 3 [les ] r [les ] 4, and one (n−2r)-cycle.

Type
Research Article
Copyright
London Mathematical Society 2001

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