Colouring polygon visibility graphs and their generalizations
James Davies, Tomasz Krawczyk, Rose McCarty, Bartosz Walczak

TL;DR
This paper establishes an upper bound on the chromatic number of curve pseudo-visibility graphs based on their clique number, providing a polynomial-time algorithm for coloring such graphs.
Contribution
It introduces a chromatic bound for curve pseudo-visibility graphs and offers a polynomial-time coloring algorithm based on ordered graph conditions.
Findings
Chromatic number is at most 3·4^{ω-1} for clique number ω.
The proof uses ordered graph conditions.
Both clique number and coloring can be computed in polynomial time.
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.
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