Coloring intersection graphs of x-monotone curves in the plane
Andrew Suk
TL;DR
This paper proves that intersection graphs of certain x-monotone curves, rays, and unit segments in the plane are chi-bounded, meaning their chromatic number can be bounded by a function of their clique number.
Contribution
It establishes chi-boundedness for intersection graphs of x-monotone curves intersecting a vertical line, extending to rays and unit segments.
Findings
Intersection graphs of x-monotone curves intersecting a vertical line are chi-bounded.
Intersection graphs of rays are chi-bounded.
Intersection graphs of unit segments are chi-bounded.
Abstract
A class of graphs G is chi-bounded if the chromatic number of the graphs in G is bounded by some function of their clique number. We show that the class of intersection graphs of simple x-monotone curves in the plane intersecting a vertical line is chi-bounded. As a corollary we show that the class of intersection graphs of rays in the plane is chi-bounded, and the class of intersection graphs of unit segments in the plane is chi-bounded
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Computational Geometry and Mesh Generation · Advanced Graph Theory Research