%0 Journal Article
%T Packing paths in a $(¦Ë+¦Ì)K_{v+u}-¦ËK_v$
%A John Asplund
%A Joe Chaffee
%A James M. Hammer
%J Mathematics
%D 2015
%I arXiv
%X 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 $(\lambda+\mu)K_{v+u}-\lambda K_v$.
%U http://arxiv.org/abs/1511.01140v1