2 Search Results for "Damásdi, Gábor"


Document
Three-Chromatic Geometric Hypergraphs

Authors: Gábor Damásdi and Dömötör Pálvölgyi

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)


Abstract
We prove that for any planar convex body C there is a positive integer m with the property that any finite point set P in the plane can be three-colored such that there is no translate of C containing at least m points of P, all of the same color. As a part of the proof, we show a strengthening of the Erdős-Sands-Sauer-Woodrow conjecture. Surprisingly, the proof also relies on the two dimensional case of the Illumination conjecture.

Cite as

Gábor Damásdi and Dömötör Pálvölgyi. Three-Chromatic Geometric Hypergraphs. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{damasdi_et_al:LIPIcs.SoCG.2022.32,
  author =	{Dam\'{a}sdi, G\'{a}bor and P\'{a}lv\"{o}lgyi, D\"{o}m\"{o}t\"{o}r},
  title =	{{Three-Chromatic Geometric Hypergraphs}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{32:1--32:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.32},
  URN =		{urn:nbn:de:0030-drops-160401},
  doi =		{10.4230/LIPIcs.SoCG.2022.32},
  annote =	{Keywords: Discrete geometry, Geometric hypergraph coloring, Decomposition of multiple coverings}
}
Document
Radon Numbers Grow Linearly

Authors: Dömötör Pálvölgyi

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)


Abstract
Define the k-th Radon number r_k of a convexity space as the smallest number (if it exists) for which any set of r_k points can be partitioned into k parts whose convex hulls intersect. Combining the recent abstract fractional Helly theorem of Holmsen and Lee with earlier methods of Bukh, we prove that r_k grows linearly, i.e., r_k ≤ c(r₂)⋅ k.

Cite as

Dömötör Pálvölgyi. Radon Numbers Grow Linearly. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 60:1-60:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{palvolgyi:LIPIcs.SoCG.2020.60,
  author =	{P\'{a}lv\"{o}lgyi, D\"{o}m\"{o}t\"{o}r},
  title =	{{Radon Numbers Grow Linearly}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{60:1--60:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.60},
  URN =		{urn:nbn:de:0030-drops-122183},
  doi =		{10.4230/LIPIcs.SoCG.2020.60},
  annote =	{Keywords: discrete geometry, convexity space, Radon number}
}
  • Refine by Author
  • 2 Pálvölgyi, Dömötör
  • 1 Damásdi, Gábor

  • Refine by Classification
  • 2 Mathematics of computing → Hypergraphs
  • 1 Theory of computation → Computational geometry

  • Refine by Keyword
  • 1 Decomposition of multiple coverings
  • 1 Discrete geometry
  • 1 Geometric hypergraph coloring
  • 1 Radon number
  • 1 convexity space
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2020
  • 1 2022

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail