@inproceedings{b733b33442f54e8c903248bf7ac54b7d,
title = "Coloring curves that cross a fixed curve",
abstract = "We prove that for every integer t ≧ 1, the class of intersection graphs of curves in the plane each of which crosses a fixed curve in at least one and at most t points is χ-bounded. This is essentially the strongest χ-boundedness result one can get for this kind of graph classes. As a corollary, we prove that for any fixed integers k ≧ 2 and t ≧ 1, every k-quasi-planar topological graph on n vertices with any two edges crossing at most t times has O(n log n) edges.",
keywords = "K-quasi-planar graphs, String graphs, χ-boundedness",
author = "Alexandre Rok and Bartosz Walczak",
note = "Funding Information: ∗ Alexandre Rok was partially supported by Israel Science Foundation grant 1136/12. Bartosz Walczak was partially supported by National Science Center of Poland grant 2015/17/D/ST1/00585. Publisher Copyright: {\textcopyright} Alexandre Rok and Bartosz Walczak.; 33rd International Symposium on Computational Geometry, SoCG 2017 ; Conference date: 04-07-2017 Through 07-07-2017",
year = "2017",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SoCG.2017.56",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "561--5615",
editor = "Katz, {Matthew J.} and Boris Aronov",
booktitle = "33rd International Symposium on Computational Geometry, SoCG 2017",
address = "Germany",
}