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Decomposing complete tripartite graphs into closed trails of arbitrary lengths

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Abstract

The complete tripartite graph K n,n,n has 3n 2 edges. For any collection of positive integers x 1, x 2,...,x m with \(\sum\limits_{i = 1}^m {x_i = 3n^2 } \) and x i ⩾ 3 for 1 ⩽ i ⩽ m, we exhibit an edge-disjoint decomposition of K n,n,n into closed trails (circuits) of lengths x 1, x 2,..., x m.

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Authors and Affiliations

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

    Elizabeth J. Billington

  2. Institute for Theoretical Computer Science ITI, Charles University, Malostranské náměstí 25, 118 00, Praha 1, Czech Republic

    Nicholas J. Cavenagh

Authors
  1. Elizabeth J. Billington
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  2. Nicholas J. Cavenagh
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Supported by Ministry of Education of the Czech Republic as project LN00A056.

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Billington, E.J., Cavenagh, N.J. Decomposing complete tripartite graphs into closed trails of arbitrary lengths. Czech Math J 57, 523–551 (2007). https://doi.org/10.1007/s10587-007-0096-y

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  • DOI: https://doi.org/10.1007/s10587-007-0096-y

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