On Galvin orientations of line graphs and list-edge-colouring
Combinatorics
2015-08-11 v1
Abstract
The notion of a Galvin orientation of a line graph is introduced, generalizing the idea used by Galvin in his landmark proof of the list-edge-colouring conjecture for bipartite graphs. If L(G) has a proper Galvin orientation with respect to k, then it immediately implies that G is k-list-edge-colourable, but the converse is not true. The stronger property is studied in graphs of the form `bipartite plus an edge', the Petersen graph, cliques, and simple graphs without odd cycles of length 5 or longer.
Keywords
Cite
@article{arxiv.1508.01820,
title = {On Galvin orientations of line graphs and list-edge-colouring},
author = {Jessica McDonald},
journal= {arXiv preprint arXiv:1508.01820},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1407.0626