Colouring polygon visibility graphs and their generalizations
Combinatorics
2021-03-16 v1 Computational Geometry
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 has chromatic number at most . 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.
Cite
@article{arxiv.2103.07803,
title = {Colouring polygon visibility graphs and their generalizations},
author = {James Davies and Tomasz Krawczyk and Rose McCarty and Bartosz Walczak},
journal= {arXiv preprint arXiv:2103.07803},
year = {2021}
}