Triangle-free intersection graphs of line segments with large chromatic number
Combinatorics
2014-12-30 v5 Computational Geometry
Discrete Mathematics
Abstract
In the 1970s, Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer , we construct a triangle-free family of line segments in the plane with chromatic number greater than . Our construction disproves a conjecture of Scott that graphs excluding induced subdivisions of any fixed graph have chromatic number bounded by a function of their clique number.
Keywords
Cite
@article{arxiv.1209.1595,
title = {Triangle-free intersection graphs of line segments with large chromatic number},
author = {Arkadiusz Pawlik and Jakub Kozik and Tomasz Krawczyk and Michał Lasoń and Piotr Micek and William T. Trotter and Bartosz Walczak},
journal= {arXiv preprint arXiv:1209.1595},
year = {2014}
}
Comments
Small corrections, bibliography update