--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Oswin foaf_name: Aichholzer, Oswin foaf_surname: Aichholzer - foaf_Person: foaf_givenName: Alan M foaf_name: Arroyo Guevara, Alan M foaf_surname: Arroyo Guevara foaf_workInfoHomepage: http://www.librecat.org/personId=3207FDC6-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0003-2401-8670 - foaf_Person: foaf_givenName: Zuzana foaf_name: Masárová, Zuzana foaf_surname: Masárová foaf_workInfoHomepage: http://www.librecat.org/personId=45CFE238-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-6660-1322 - foaf_Person: foaf_givenName: Irene foaf_name: Parada, Irene foaf_surname: Parada - foaf_Person: foaf_givenName: Daniel foaf_name: Perz, Daniel foaf_surname: Perz - foaf_Person: foaf_givenName: Alexander foaf_name: Pilz, Alexander foaf_surname: Pilz - foaf_Person: foaf_givenName: Josef foaf_name: Tkadlec, Josef foaf_surname: Tkadlec foaf_workInfoHomepage: http://www.librecat.org/personId=3F24CCC8-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-1097-9684 - foaf_Person: foaf_givenName: Birgit foaf_name: Vogtenhuber, Birgit foaf_surname: Vogtenhuber bibo_doi: 10.7155/jgaa.00591 bibo_issue: '2' bibo_volume: 26 dct_date: 2022^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/1526-1719 dct_language: eng dct_publisher: Brown University@ dct_title: On compatible matchings@ ...