@article{3e49cc83a3884d0ea35bd02fe84c5d73,
title = "Outerstring graphs are χ-bounded",
abstract = "An outerstring graph is an intersection graph of curves that lie in a common half-plane and have one endpoint on the boundary of that half-plane. We prove that the class of outerstring graphs is χ-bounded, which means that their chromatic number is bounded by a function of their clique number. This generalizes a series of previous results on χ-boundedness of outerstring graphs with various additional restrictions on the shape of curves or the number of times the pairs of curves can cross. The assumption that each curve has an endpoint on the boundary of the half-plane is justified by the known fact that triangle-free intersection graphs of straight-line segments can have arbitrarily large chromatic number.",
keywords = "Chromatic number, Geometric intersection graphs, String graphs, χ-boundedness",
author = "Alexandre Rok and Bartosz Walczak",
note = "Funding Information: The first author was partially supported by Swiss National Science Foundation grants 200020-144531 and 200021-137574 and by Israel Science Foundation grant 1136/12. The second author was partially supported by Swiss National Science Foundation grant 200020-144531, by Ministry of Science and Higher Education of Poland grant 884/N-ESF-EuroGIGA/10/2011/0 within ESF EuroGIGA project GraDR, and by National Science Centre of Poland grant 2015/17/D/ST1/00585.*%blankline%* Funding Information: ∗Received by the editors November 17, 2017; accepted for publication (in revised form) July 26, 2019; published electronically November 14, 2019. A preliminary version of this paper appeared in Proceedings of the 30th Annual Symposium on Computational Geometry (SoCG 2014), Siu-Wing Cheng and Olivier Devillers, eds., ACM, New York, pp. 136–143. https://doi.org/10.1137/17M1157374 Funding: The first author was partially supported by Swiss National Science Foundation grants 200020-144531 and 200021-137574 and by Israel Science Foundation grant 1136/12. The second author was partially supported by Swiss National Science Foundation grant 200020-144531, by Ministry of Science and Higher Education of Poland grant 884/N-ESF-EuroGIGA/10/2011/0 within ESF Eu-roGIGA project GraDR, and by National Science Centre of Poland grant 2015/17/D/ST1/00585. Publisher Copyright: {\textcopyright} 2019 Alexandre Rok and Bartosz Walczak.",
year = "2019",
month = jan,
day = "1",
doi = "10.1137/17M1157374",
language = "English",
volume = "33",
pages = "2181--2199",
journal = "SIAM Journal on Discrete Mathematics",
issn = "0895-4801",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}