Decomposition of a complete bipartite multigraph into arbitrary cycle sizes

John Asplund, Joe Chaffee, James Hammer

In a graph $G$, let ${\mu }_G(xy)$ denote the number of edges between $x$ and $y$ in $G$. Let $\lambda K_{v,u}$ be the graph $(V\cup U,E)$ with $|V|=v$, $|U|=u$, and \[ μ_G(xy)=\begin{cases} λ…