Extension from Precoloured Sets of Edges
Combinatorics
2018-05-29 v3
Abstract
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 . 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.
Cite
@article{arxiv.1407.4339,
title = {Extension from Precoloured Sets of Edges},
author = {Katherine Edwards and António Girão and Jan van den Heuvel and Ross J. Kang and Gregory J. Puleo and Jean-Sébastien Sereni},
journal= {arXiv preprint arXiv:1407.4339},
year = {2018}
}
Comments
26 pages, 3 figures, 1 table; in v2, two co-authors added, main conjecture weakened, weak version of conjecture proved, planar section updated; v3 accepted to Electronic Journal of Combinatorics