The generalized almost resolvable cycle system problem |
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Authors: | Peter Adams Elizabeth J. Billington D. G. Hoffman C. C. Lindner |
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Affiliation: | 1. Department of Mathematics, The University of Queensland, Brisbane St Lucia, Qld, 4072, Australia 2. Department of Mathematics and Statistics Parker Hall, Auburn University, Auburn, AL, 36849, USA
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Abstract: | Let (X, C) be a k-cycle system of order n, with vertex set X (of cardinality n) and collection of k-cycles C. Suppose n=kq+r where r<k. An almost parallel class of C is a collection of q=(n−r)/k pairwise vertex-disjoint k-cycles of C. Each almost parallel class thus will miss r of the n vertices in X. The k-cycle system (X,C) is said to be almost resolvable if C can be partitioned into almost parallel classes such that the remaining k-cycles are vertex disjoint. (These remaining k-cycles are referred to as a short parallel class.) |
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