License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2017.56
URN: urn:nbn:de:0030-drops-71788
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Rok, Alexandre ; Walczak, Bartosz

Coloring Curves That Cross a Fixed Curve

LIPIcs-SoCG-2017-56.pdf (0.5 MB)


We prove that for every integer t greater than or equal to 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 chi-bounded. This is essentially the strongest chi-boundedness result one can get for this kind of graph classes. As a corollary, we prove that for any fixed integers k > 1 and t > 0, every k-quasi-planar topological graph on n vertices with any two edges crossing at most t times has O(n log n) edges.

BibTeX - Entry

  author =	{Alexandre Rok and Bartosz Walczak},
  title =	{{Coloring Curves That Cross a Fixed Curve}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{56:1--56:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-71788},
  doi =		{10.4230/LIPIcs.SoCG.2017.56},
  annote =	{Keywords: String graphs, chi-boundedness, k-quasi-planar graphs}

Keywords: String graphs, chi-boundedness, k-quasi-planar graphs
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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