Extension from Precoloured Sets of Edges
Katherine Edwards, António Girão, Jan van den Heuvel, Ross J. Kang, Gregory J. Puleo, Jean‐Sébastien Sereni · The Electronic Journal of Combinatorics · 2018
We consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum degree $\Delta$. We are especially interested in the following question: when is it possible to extend a precoloured matching to a colouring of all edges of a (multi)graph? This question turns out to be related to the notorious List Colouring Conjecture and other classic notions of choosability.