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.
Source: wiktionary
Precoloring
Synonyms for "precoloring"
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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.
Source: wiktionary
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