Perfect Matchings with Crossings

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

Perfect Matchings with Crossings

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

Institute of Software Technology (7160)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

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
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
Abbreviated title	CG:YRF
City	Virtuell
Period	7/06/21 → 9/06/21

Access to Document

https://cse.buffalo.edu/socg21/files/YRF-Booklet.pdf#page=24Licence: Other

Cite this

@inproceedings{00e3eb460b784012b7276268cc9ab725,

title = "Perfect Matchings with Crossings",

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.",

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

year = "2021",

language = "English",

pages = "24--27",

booktitle = "Proceedings of the Computational Geometry: Young Researchers Forum",

note = "2021 Computational Geometry: Young Researchers Forum : CG:YRF 2021, CG:YRF ; Conference date: 07-06-2021 Through 09-06-2021",

}

TY - GEN

T1 - Perfect Matchings with Crossings

AU - Aichholzer, Oswin

AU - Fabila-Monroy, Ruy

AU - Kindermann, Philipp

AU - Parada, Irene

AU - Paul, Rosna

AU - Perz, Daniel

AU - Schnider, Patrick

AU - Vogtenhuber, Birgit

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

M3 - Conference paper

SP - 24

EP - 27

BT - Proceedings of the Computational Geometry: Young Researchers Forum

T2 - 2021 Computational Geometry: Young Researchers Forum

Y2 - 7 June 2021 through 9 June 2021

ER -

Perfect Matchings with Crossings

Abstract

Conference

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Cite this