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arXiv · 2103.07803

Colouring polygon visibility graphs and their generalizations

James Davies·Tomasz Krawczyk·Rose McCarty·Bartosz Walczak
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Abstract

Curve pseudo-visibility graphs generalize polygon and pseudo-polygon visibility graphs and form a hereditary class of graphs. We prove that every curve pseudo-visibility graph with clique number $\omega$ has chromatic number at most $3\cdot 4^{\omega-1}$. The proof is carried through in the setting of ordered graphs; we identify two conditions satisfied by every curve pseudo-visibility graph (considered as an ordered graph) and prove that they are sufficient for the claimed bound. The proof is algorithmic: both the clique number and a colouring with the claimed number of colours can be computed in polynomial time.

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James Davies, Tomasz Krawczyk, Rose McCarty, Bartosz Walczak. 2021-03-13. Colouring polygon visibility graphs and their generalizations. https://arxiv.org/abs/2103.07803

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