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Graphs of bounded cliquewidth are polynomially $χ$-bounded (1910.00697v3)
Published 1 Oct 2019 in cs.DM and math.CO
Abstract: We prove that if $\mathcal{C}$ is a hereditary class of graphs that is polynomially $\chi$-bounded, then the class of graphs that admit decompositions into pieces belonging to $\mathcal{C}$ along cuts of bounded rank is also polynomially $\chi$-bounded. In particular, this implies that for every positive integer $k$, the class of graphs of cliquewidth at most $k$ is polynomially $\chi$-bounded.
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