Perfect Matchings with Crossings

Oswin Aichholzer, Ruy Fabila-Monroy, Philipp Kindermann, Irene Parada, Rosna Paul, Daniel Perz, Patrick Schnider, Birgit Vogtenhuber

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


In this paper, we analyze the number of straight-line perfect matchings with $k$ crossings on point sets of size $n$ = $2m$ in general position. We show that for every $kn/8-1)$, every $n$-point set admits a perfect matching with exactly $k$ crossings and that there exist $n$-point sets where every perfect matching has fewer than $5n^2/72$ crossings. We also study the number of perfect matchings with at most $k$ crossings. Finally we show that convex point sets %in convex position maximize the number of perfect matchings with $n/2 $ crossings and $n/2 -1$ crossings.
Original languageEnglish
Title of host publicationProceedings of the Computational Geometry: Young Researchers Forum
Number of pages4
Publication statusPublished - 2021
Event2021 Computational Geometry: Young Researchers Forum: CG:YRF 2021 - Virtuell
Duration: 7 Jun 20219 Jun 2021


Conference2021 Computational Geometry: Young Researchers Forum
Abbreviated titleCG:YRF


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