Extension from Precoloured Sets of Edges

  • Katherine Edwards
  • António Girão
  • Jan van den Heuvel
  • Ross J. Kang
  • Gregory J. Puleo
  • Jean-Sébastien Sereni
Keywords: Edge-colouring, Precolouring extension, Multigraphs, List colouring


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.

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