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On the Volume of 4-Cycle Trades

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Abstract.

 A 4-cycle trade of volume t corresponds to a simple graph G without isolated vertices, where the edge set can be partitioned into t 4-cycles in at least two different ways such that the two collections of 4-cycles have no 4-cycles in common. The foundation of the trade is v=|V(G)|. This paper determines for which values of t and v there exists a 4-cycle trade of volume t and foundation v.

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Authors and Affiliations

  1. Centre for Discrete Mathematics and Computing, Department of Mathematics, The University of Queensland, Qld 4072, Australia, , , , , , AU

    Darryn Bryant

  2. Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK, e-mail: B.M.Maenhaut@open.ac.uk, , , , , , GB

    Mike Grannell, Terry Griggs & Barbara Maenhaut

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  1. Darryn Bryant
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  2. Mike Grannell
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  3. Terry Griggs
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  4. Barbara Maenhaut
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Received: September 16, 2000 Final version received: October 2, 2001

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Bryant, D., Grannell, M., Griggs, T. et al. On the Volume of 4-Cycle Trades. Graphs and Combinatorics 19, 53–63 (2003). https://doi.org/10.1007/s00373-002-0484-x

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  • DOI: https://doi.org/10.1007/s00373-002-0484-x

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