eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-06-06
59:1
59:14
10.4230/LIPIcs.SoCG.2024.59
article
A Structure Theorem for Pseudo-Segments and Its Applications
Fox, Jacob
1
Pach, János
2
Suk, Andrew
3
Department of Mathematics, Stanford University, CA, USA
HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
Department of Mathematics, University of California San Diego, La Jolla, CA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol293-socg2024/LIPIcs.SoCG.2024.59/LIPIcs.SoCG.2024.59.pdf
Regularity lemma
pseudo-segments
intersection graphs