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Clustered colouring of graph classes with bounded treedepth or pathwidth
Published online by Cambridge University Press: 05 July 2022
Abstract
The clustered chromatic number of a class of graphs is the minimum integer
$k$
such that for some integer
$c$
every graph in the class is
$k$
-colourable with monochromatic components of size at most
$c$
. 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.
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- © The Author(s), 2022. Published by Cambridge University Press
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