DROPS

Document

DOI: 10.4230/LIPIcs.SoCG.2017.56

Coloring Curves That Cross a Fixed Curve

Authors: Alexandre Rok and Bartosz Walczak

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

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

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)

Copy BibTex To Clipboard

@InProceedings{rok_et_al:LIPIcs.SoCG.2017.56,
  author =	{Rok, Alexandre and Walczak, Bartosz},
  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 =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.56},
  URN =		{urn:nbn:de:0030-drops-71788},
  doi =		{10.4230/LIPIcs.SoCG.2017.56},
  annote =	{Keywords: String graphs, chi-boundedness, k-quasi-planar graphs}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2016.59

Weak 1/r-Nets for Moving Points

Authors: Alexandre Rok and Shakhar Smorodinsky

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract

In this paper, we extend the weak 1/r-net theorem to a kinetic setting where the underlying set of points is moving polynomially with bounded description complexity. We establish that one can find a kinetic analog N of a weak 1/r-net of cardinality O(r^(d(d+1)/2)log^d r) whose points are moving with coordinates that are rational functions with bounded description complexity. Moreover, each member of N has one polynomial coordinate.

Cite as

Alexandre Rok and Shakhar Smorodinsky. Weak 1/r-Nets for Moving Points. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 59:1-59:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{rok_et_al:LIPIcs.SoCG.2016.59,
  author =	{Rok, Alexandre and Smorodinsky, Shakhar},
  title =	{{Weak 1/r-Nets for Moving Points}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{59:1--59:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.59},
  URN =		{urn:nbn:de:0030-drops-59514},
  doi =		{10.4230/LIPIcs.SoCG.2016.59},
  annote =	{Keywords: Hypergraphs, Weak epsilon-net}
}

Search Results

Documents authored by Rok, Alexandre

Coloring Curves That Cross a Fixed Curve

Abstract

Cite as

Weak 1/r-Nets for Moving Points

Abstract

Cite as

Thanks for your feedback!

Could not send message