Coloring polygon visibility graphs and their generalizations.

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 3 center dot 4(omega-1). The proof is carried through in the setting of ordered graphs; we identify two conditions satisfied by every curve pseudovisibility 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 coloring with the claimed number of colors can be computed in polynomial time. (c) 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).