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Clustered colouring of graph classes with bounded treedepth or pathwidth

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arxiv 2012.05554 v2 pith:DHODBREY submitted 2020-12-10 math.CO

classification math.CO
keywords classclusteredchromaticnumberboundedminor-closeddetermineevery
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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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