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Resolvable and near-resolvable decompositions ofDK v into oriented 4-cycles

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Summary

A resolvableX-decomposition ofDK v (the complete symmetric digraph onv vertices) is a partition of the arcs ofDK v into isomorphic factors where each factor is a vertex-disjoint union of copies ofX and spans all vertices ofDK v . There are four orientations ofC 4 (the 4-cycle), only one of which has been considered: Bennett and Zhang, Aequationes Math.40 (1990), 248–260. We give necessary and sufficient conditions onv for resolvableX-decomposition ofDK v , whereX is any one of the other three orientations ofC 4. A near-resolvableX-decomposition ofDK v is as above except that each factor spans all but one vertex ofDK v . Again, one orientation ofC 4 has been dealt with by Bennett and Zhang, and we provide necessary and sufficient conditions onv for the remaining three cases. The construction techniques used are both direct (for small values ofv) and recursive.

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Authors and Affiliations

  1. Department of Science and Mathematics, Douglas College, New Westminster, British Columbia, Canada

    Susan Hamm & Katherine Heinrich

  2. Department of Mathematics and Stastics, Simon Fraser University, V5A 156, Burnaby, British Columbia, Canada

    Susan Hamm & Katherine Heinrich

Authors
  1. Susan Hamm
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  2. Katherine Heinrich
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Additional information

The author thanks Simon Fraser University for its support during her graduate studies when the research for this paper was undertaken.

The author acknowledges the Natural Sciences and Engineering Research Council of Canada for financial support under grant A-7829.

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Hamm, S., Heinrich, K. Resolvable and near-resolvable decompositions ofDK v into oriented 4-cycles. Aeq. Math. 44, 304–316 (1992). https://doi.org/10.1007/BF01830987

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  • DOI: https://doi.org/10.1007/BF01830987

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