Twisted Ways to Find Plane Structures in Simple Drawings of Complete Graphs

Oswin Aichholzer, Alfredo García, Javier Tejel, Birgit Vogtenhuber, Alexandra Weinberger*

*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandBegutachtung


Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). We introduce a special kind of simple drawings that we call generalized twisted rawings. A simple drawing is generalized twisted if there is a point O such that every ray emanating from O crosses every edge of the rawing at most once and there is a ray emanating from O which crosses every edge exactly once.
Via this new class of simple drawings, we show that every simple drawing of the complete graph with n vertices contains Ω(n1/2) pairwise disjoint edges and a plane path of length Ω(log n / log log n). Both results improve over previously known best lower bounds. On the way we show several structural results about and properties of generalized twisted drawings. We further present different characterizations of generalized twisted drawings, which might be of independent interest.
Titel38th International Symposium on Computational Geometry (SoCG 2022)
PublikationsstatusVeröffentlicht - 2022
Veranstaltung38th International Symposium on Computational Geometry: SoCG 2022 - Berlin, Germany, Berlin, Deutschland
Dauer: 7 Juni 202210 Juni 2022


Konferenz38th International Symposium on Computational Geometry
KurztitelSoCG 2022

Fields of Expertise

  • Information, Communication & Computing


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