Coloring Curves That Cross a Fixed Curve

Rok, Alexandre; Walczak, Bartosz

doi:10.4230/LIPIcs.SoCG.2017.56

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Coloring Curves That Cross a Fixed Curve

Authors Alexandre Rok, Bartosz Walczak

Part of: Volume: 33rd International Symposium on Computational Geometry (SoCG 2017)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Computational Geometry (SoCG)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2017-06-20

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Document Identifiers

DOI: 10.4230/LIPIcs.SoCG.2017.56
URN: urn:nbn:de:0030-drops-71788

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Keywords

String graphs
chi-boundedness
k-quasi-planar graphs

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Abstract

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.

Cite As Get BibTex

Alexandre Rok and Bartosz Walczak. Coloring Curves That Cross a Fixed Curve. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 56:1-56:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.SoCG.2017.56

Author Details

Alexandre Rok

Bartosz Walczak

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