Clustered colouring of graph classes with bounded treedepth or pathwidth
Combinatorics
2022-01-24 v2
Abstract
The "clustered chromatic number" of a class of graphs is the minimum integer such that for some integer every graph in the class is -colourable with monochromatic components of size at most . We determine the clustered chromatic number of any minor-closed class with bounded treedepth, and prove a best possible upper bound on the clustered chromatic number of any minor-closed class with bounded pathwidth. As a consequence, we determine the fractional clustered chromatic number of every minor-closed class.
Cite
@article{arxiv.2012.05554,
title = {Clustered colouring of graph classes with bounded treedepth or pathwidth},
author = {Sergey Norin and Alex Scott and David R. Wood},
journal= {arXiv preprint arXiv:2012.05554},
year = {2022}
}