  Following standard terminology, $\lambda K_v$ is a multigraph on $v$ vertices
such that $\lambda$ edges join each pair of vertices. Let
$(\lambda+\mu)K_{v+u}-\lambda K_v$ be the graph $(V\cup U,E)$ with $|V|=v$,
$|U|=u$, and $(\lambda+\mu)-\lambda=\mu$ edges between the vertices $x$ and $y$
if $x$ and $y$ both lie in $V$ and $\lambda+\mu$ edges between $x$ and $y$
otherwise. The main result of this paper establishes necessary and sufficient
conditions for an $m$-path decomposition of $(\lambda+\mu)K_{v+u}-\lambda K_v$.
