Colouring polygon visibility graphs and their generalizations

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 $\omega$ 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.