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arXiv · 1910.00697

Graphs of bounded cliquewidth are polynomially $\chi$-bounded

Marthe Bonamy·Michał Pilipczuk
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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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Marthe Bonamy, Michał Pilipczuk. 2019-10-01. Graphs of bounded cliquewidth are polynomially $\chi$-bounded. https://arxiv.org/abs/1910.00697

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