Colouring triangle-free graphs with local list sizes
Combinatorics
2021-03-05 v2 Discrete Mathematics
Abstract
We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow-up work of Bernshteyn) on the (list) chromatic number of triangle-free graphs. In both our results, we permit the amount of colour made available to vertices of lower degree to be accordingly lower. One result concerns list colouring and correspondence colouring, while the other concerns fractional colouring. Our proof of the second illustrates the use of the hard-core model to prove a Johansson-type result, which may be of independent interest.
Cite
@article{arxiv.1812.01534,
title = {Colouring triangle-free graphs with local list sizes},
author = {Ewan Davies and Rémi de Joannis de Verclos and Ross J. Kang and François Pirot},
journal= {arXiv preprint arXiv:1812.01534},
year = {2021}
}
Comments
16 pages; v2 includes minor corrections after review; to appear in Random Structures & Algorithms