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Title: A Structure Theorem for Pseudo-Segments and Its Applications
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.  more » « less
Award ID(s):
2246847
PAR ID:
10539280
Author(s) / Creator(s):
; ;
Editor(s):
Mulzer, Wolfgang; Phillips, Jeff M
Publisher / Repository:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Date Published:
Volume:
293
ISSN:
1868-8969
ISBN:
978-3-95977-316-4
Page Range / eLocation ID:
293-293
Subject(s) / Keyword(s):
Regularity lemma pseudo-segments intersection graphs Mathematics of computing → Combinatorics
Format(s):
Medium: X Size: 14 pages; 727382 bytes Other: application/pdf
Size(s):
14 pages 727382 bytes
Right(s):
Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
Sponsoring Org:
National Science Foundation
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