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Clustered colouring of graph classes with bounded treedepth or pathwidth

Part of: Graph theory

Published online by Cambridge University Press:  05 July 2022

Sergey Norin ,
Alex Scott  and
David R. Wood
Sergey Norin
Affiliation:
Department of Mathematics and Statistics, McGill University, Montréal, Canada. Supported by NSERC grant 418520
Alex Scott
Affiliation:
Mathematical Institute, University of Oxford, Oxford, UK
David R. Wood*
Affiliation:
School of Mathematics, Monash University, Melbourne, Australia. Supported by the Australian Research Council
*
*Corresponding author. Email: david.wood@monash.edu
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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.

Keywords

graphgraph colouringclustered colouringminortreedepthpathwidthfractional colouring

MSC classification

Primary: 05C83: Graph minors
Secondary: 05C15: Coloring of graphs and hypergraphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 32 , Issue 1 , January 2023 , pp. 122 - 133
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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