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Abstract
A matching is compatible to two or more labeled point sets of size n with labels { 1, ⋯, n} if its straightline drawing on each of these point sets is crossingfree. 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 convex sets of n points there exists a compatible matching with ⌊2n⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n ^{1} ^{/} ^{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(n ^{2} ^{/} ^{(} ^{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 a labeling such that any compatible matching consists only of a single edge.
Original language  English 

Title of host publication  WALCOM 
Subtitle of host publication  Algorithms and Computation  15th International Conference and Workshops, WALCOM 2021, Proceedings 
Editors  Ryuhei Uehara, SeokHee Hong, Subhas C. Nandy 
Pages  221233 
Number of pages  13 
DOIs  
Publication status  Published  2021 
Publication series
Name  Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 

Volume  12635 LNCS 
ISSN (Print)  03029743 
ISSN (Electronic)  16113349 
Keywords
 Compatible graphs
 Crossingfree matchings
 Geometric graphs
ASJC Scopus subject areas
 Theoretical Computer Science
 Computer Science(all)
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Dive into the research topics of 'On Compatible Matchings'. Together they form a unique fingerprint.Activities
 1 Talk at conference or symposium

On Compatible Matchings
Daniel Perz (Speaker)
2021Activity: Talk or presentation › Talk at conference or symposium › Science to science
Prizes

Best Paper Award WALCOM 2021
Perz, D. (Recipient), Aichholzer, Oswin (Recipient), Vogtenhuber, Birgit (Recipient), De Parada, I. M. (Recipient), Arroyo, A. (Recipient), Masárová, Z. (Recipient), Tkadlec, J. (Recipient) & Pilz, A. (Recipient), 2021
Prize: Prizes / Medals / Awards