# Path and cycle decompositions of complete equipartite graphs: Four parts

Billington, Elizabeth J., Cavenagh, Nicholas J. and Smith, Benjamin R. (2009) Path and cycle decompositions of complete equipartite graphs: Four parts. Discrete Mathematics, 309 10: 3061-3073. doi:10.1016/j.disc.2008.08.009

Author Billington, Elizabeth J.Cavenagh, Nicholas J.Smith, Benjamin R. Path and cycle decompositions of complete equipartite graphs: Four parts Discrete Mathematics   Check publisher's open access policy 0012-365X1872-681X 2009-05-28 2008 Article (original research) 10.1016/j.disc.2008.08.009 Not yet assessed 309 10 3061 3073 13 D. B. West Amsterdam, The Netherlands Elsevier eng C1970101 Expanding Knowledge in the Mathematical Sciences010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) We show that a complete equipartite graph with four partite sets has an edge-disjoint decomposition into cycles of length k if and only if k >= 3, the partite set size is even, k divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least k. We also show that a complete equi partite graph with four even partite sets has an edge-disjoint decomposition into paths with k edges if and only if k divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least k + 1. (C) 2008 Elsevier B.V. All rights reserved. We show that a complete equipartite graph with four partite sets has an edge-disjoint decomposition into cycles of length k if and only if k≥3, the partite set size is even, k divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least k. We also show that a complete equipartite graph with four even partite sets has an edge-disjoint decomposition into paths with k edges if and only if k divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least k+1. Complete equipartite graphPath decompositionCycle decomposition C1 Provisional Code UQ

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