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Decomposing Complete Equipartite Graphs into Closed Trails of Length k

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Abstract

Necessary conditions for a simple connected graph G to admit a decomposition into closed trails of length k ≥ 3 are that G is even and its total number of edges is a multiple of k. In this paper we show that these conditions are sufficient in the case when G is the complete equipartite graph having at least three parts, each of the same size.

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Authors and Affiliations

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

    Benjamin R. Smith

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  1. Benjamin R. Smith
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Correspondence to Benjamin R. Smith.

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Smith, B.R. Decomposing Complete Equipartite Graphs into Closed Trails of Length k . Graphs and Combinatorics 26, 133–140 (2010). https://doi.org/10.1007/s00373-010-0899-8

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  • DOI: https://doi.org/10.1007/s00373-010-0899-8

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