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.