Circle graphs are quadratically $\chi$-bounded

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arxiv 1905.11578 v1 pith:DGAEEXUB submitted 2019-05-28 math.CO

James Davies , Rose McCarty This is my paper · ORCID

classification math.CO

keywords circlenumberomegaboundedchromaticcliquegraphgraphs

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abstract

We prove that the chromatic number of a circle graph with clique number $\omega$ is at most $7\omega^2$.

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Coloring Hasse diagrams and disjointness graphs of curves
math.CO 2019-08 accept novelty 7.0 of 10

For every girth r, there are n curves whose disjointness graph has girth at least r and chromatic number at least a constant times (1/r) log n, improving Bollobás's bound and matching it for uniquely generated posets.