Decomposing Complete Equipartite Graphs into Closed Trails of Length k |
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| Authors: | Benjamin R. Smith |
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| Affiliation: | 1. Department of Mathematics, Centre for Discrete Mathematics and Computing, The University of Queensland, Brisbane, QLD, 4072, Australia
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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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