  Edwards, van den Heuvel, Kang, and Sereni conjectured the following
strengthening of Vizing's Theorem: let $G$ be a simple graph, and let $K =
\Delta(G) + 1$. For any matching $M$ in $G$ and any precoloring of the edges in
$M$ using the colors $\{1, \ldots, K\}$, there is some proper $K$-edge-coloring
of $G$ extending the given precoloring. We give an infinite family of
counterexamples to this conjecture, and prove a weaker version of the
conjecture proposed in the same work.
