Smith, B.R. & Cavenagh, N.J. (2010). Decomposing complete equipartite graphs into short odd cycles. The Electronic Journal of Combinatorics, 17(1), #R130.
Permanent Research Commons link: http://hdl.handle.net/10289/4781
In this paper we examine the problem of decomposing the lexicographic product of a cycle with an empty graph into cycles of uniform length. We determine necessary and sufficient conditions for a solution to this problem when the cycles are of odd length. We apply this result to find necessary and sufficient conditions to decompose a complete equipartite graph into cycles of uniform length, in the case that the length is both odd and short relative to the number of parts.
First published in The Electronic Journal of Combinatorics in Volume 17 number 1, 2010, published by the American Mathematical Society.