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

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

Abstract

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.
Original languageEnglish
Title of host publication38th International Symposium on Computational Geometry (SoCG 2022)
Pages5:1--5:18
Number of pages18
Publication statusPublished - 2022
Event38th International Symposium on Computational Geometry: SoCG 2022 - Berlin, Germany, Berlin, Germany
Duration: 7 Jun 202210 Jun 2022
https://www.inf.fu-berlin.de/inst/ag-ti/socg22/socg.html

Conference

Conference38th International Symposium on Computational Geometry
Abbreviated titleSoCG 2022
Country/TerritoryGermany
CityBerlin
Period7/06/2210/06/22
Internet address

Fields of Expertise

  • Information, Communication & Computing

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