English

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 ω\omega has chromatic number at most 34ω13\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.

Keywords

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}
}
R2 v1 2026-06-24T00:06:55.019Z