---
_id: '11938'
abstract:
- lang: eng
text: A matching is compatible to two or more labeled point sets of size n with
labels {1, . . . , n} if its straight-line drawing on each of these point sets
is crossing-free. We study the maximum number of edges in a matching compatible
to two or more labeled point sets in general position in the plane. We show that
for any two labeled sets of n points in convex position there exists a compatible
matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets
we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound,
we use probabilistic arguments to show that for any ℓ given sets of n points there
exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1))
edges. Finally, we show that Θ(log n) copies of any set of n points are necessary
and sufficient for the existence of labelings of these point sets such that any
compatible matching consists only of a single edge.
acknowledgement: 'A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411.
Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative
DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported
by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by
ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23
(RiSE).'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Alan M
full_name: Arroyo Guevara, Alan M
id: 3207FDC6-F248-11E8-B48F-1D18A9856A87
last_name: Arroyo Guevara
orcid: 0000-0003-2401-8670
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Irene
full_name: Parada, Irene
last_name: Parada
- first_name: Daniel
full_name: Perz, Daniel
last_name: Perz
- first_name: Alexander
full_name: Pilz, Alexander
last_name: Pilz
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
ama: Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings.
Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591
apa: Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D.,
Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph
Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591
chicago: Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada,
Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible
Matchings.” Journal of Graph Algorithms and Applications. Brown University,
2022. https://doi.org/10.7155/jgaa.00591.
ieee: O. Aichholzer et al., “On compatible matchings,” Journal of Graph
Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240,
2022.
ista: Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec
J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and
Applications. 26(2), 225–240.
mla: Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms
and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591.
short: O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz,
J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022)
225–240.
corr_author: '1'
date_created: 2022-08-21T22:01:56Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2026-04-16T09:18:20Z
day: '01'
ddc:
- '000'
department:
- _id: UlWa
- _id: HeEd
- _id: KrCh
doi: 10.7155/jgaa.00591
ec_funded: 1
external_id:
arxiv:
- '2101.03928'
file:
- access_level: open_access
checksum: dc6e255e3558faff924fd9e370886c11
content_type: application/pdf
creator: dernst
date_created: 2022-08-22T06:42:42Z
date_updated: 2022-08-22T06:42:42Z
file_id: '11940'
file_name: 2022_JourGraphAlgorithmsApplic_Aichholzer.pdf
file_size: 694538
relation: main_file
success: 1
file_date_updated: 2022-08-22T06:42:42Z
fulldoi: https://doi.org/10.7155/jgaa.00591
has_accepted_license: '1'
intvolume: ' 26'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: 225-240
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
publication: Journal of Graph Algorithms and Applications
publication_identifier:
issn:
- 1526-1719
publication_status: published
publisher: Brown University
quality_controlled: '1'
related_material:
record:
- id: '9296'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: On compatible matchings
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 26
year: '2022'
...