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A Structure Theorem for Pseudo-Segments and Its Applications

Authors Jacob Fox, János Pach, Andrew Suk

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Author Details

Jacob Fox
  • Department of Mathematics, Stanford University, CA, USA
János Pach
  • HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
Andrew Suk
  • Department of Mathematics, University of California San Diego, La Jolla, CA, USA

Funding

  • Fox, Jacob: Supported by NSF Award DMS-2154129.
  • Pach, János: Rényi Institute, Budapest. Supported by NKFIH grant K-176529, Austrian Science Fund Z 342-N31 and ERC Advanced Grant "GeoScape."
  • Suk, Andrew: Supported by NSF CAREER award DMS-1800746, and NSF awards DMS-1952786 and DMS-2246847.

Cite AsGet BibTex

Jacob Fox, János Pach, and Andrew Suk. A Structure Theorem for Pseudo-Segments and Its Applications. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 59:1-59:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SoCG.2024.59

Abstract

We prove a far-reaching strengthening of Szemerédi’s regularity lemma for intersection graphs of pseudo-segments. It shows that the vertex set of such graphs can be partitioned into a bounded number of parts of roughly the same size such that almost all of the bipartite graphs between pairs of parts are complete or empty. We use this to get an improved bound on disjoint edges in simple topological graphs, showing that every n-vertex simple topological graph with no k pairwise disjoint edges has at most n(log n)^O(log k) edges.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics
Keywords
  • Regularity lemma
  • pseudo-segments
  • intersection graphs

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References

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