Precoloring

For any matching M in G and any precoloring of the edges in M using the colors #92;#123;1,#92;ldots,K#92;#125;, there is some proper K-edge-coloring of G extending the given precoloring.

On the other hand, Thomassen's proof on planar graph 5 - choosability shows that some precolorings (two adjacent precolored vertices) and short lists (on the same face) allow a list coloring extension.