Resolvably Decomposing Complete Equipartite Graphs Minus a One-Factor into Cycles of Uniform Even Length

Abstract

We seek a decomposition of a complete equipartite graph minus
a one-factor into parallel classes each consisting of cycles of length
$k$. In this paper, we address the problem of resolvably decomposing
complete multipartite graphs with $r$ parts each of size $\alpha$ with a one-
factor removed into $k$-cycles. We find the necessary conditions, and
give solutions for even cycle lengths.