Bichromatic Perfect Matchings with Crossings

09/01/2023

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by   Oswin Aichholzer, et al.

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We consider bichromatic point sets with n red and n blue points and study straight-line bichromatic perfect matchings on them. We show that every such point set in convex position admits a matching with at least 3n^2/8-n/2+c crossings, for some -1/2≤ c ≤1/8. This bound is tight since for any k> 3n^2/8 -n/2+1/8 there exist bichromatic point sets that do not admit any perfect matching with k crossings.