@inproceedings{9296,
  abstract     = { 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 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(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(logn)  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.},
  author       = {Aichholzer, Oswin and Arroyo Guevara, Alan M and Masárová, Zuzana and Parada, Irene and Perz, Daniel and Pilz, Alexander and Tkadlec, Josef and Vogtenhuber, Birgit},
  booktitle    = {15th International Conference on Algorithms and Computation},
  isbn         = {9783030682101},
  issn         = {16113349},
  location     = {Yangon, Myanmar},
  pages        = {221--233},
  publisher    = {Springer Nature},
  title        = {{On compatible matchings}},
  doi          = {10.1007/978-3-030-68211-8_18},
  volume       = {12635},
  year         = {2021},
}