Abstract
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 language | English |
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Title of host publication | Proceedings of the Computational Geometry: Young Researchers Forum |
Pages | 24-27 |
Number of pages | 4 |
Publication status | Published - 2021 |
Event | 2021 Computational Geometry: Young Researchers Forum: CG:YRF 2021 - Virtuell Duration: 7 Jun 2021 → 9 Jun 2021 |
Conference
Conference | 2021 Computational Geometry: Young Researchers Forum |
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Abbreviated title | CG:YRF |
City | Virtuell |
Period | 7/06/21 → 9/06/21 |