precoloring

pre- +‎ coloring

precoloring (countable and uncountable, plural precolorings)

1. coloring in advance
   • 2015, Gregory J. Puleo, “On an Edge Precoloring Conjecture”, in arXiv‎:

     For any matching ${\displaystyle M}$ in ${\displaystyle G}$ and any precoloring of the edges in ${\displaystyle M}$ using the colors ${\displaystyle \{1,\ldots ,K\}}$, there is some proper ${\displaystyle K}$-edge-coloring of ${\displaystyle G}$ extending the given precoloring.

2. A particular assignment of colors in a precoloring.
   • 1999, Ronald L. Graham, Contemporary Trends in Discrete Mathematics: From DIMACS and DIMATIA to the Future : DIMATIA-DIMACS Conference, Page 187:

     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.