O. Aichholzer, S. Felsner, R. Paul, M. Scheucher, and B. Vogtenhuber
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
$$#12#>frac{3n^2}{8}-#17#>frac{n}{2}+c$$3n28-n2+ccrossings,
for some $$ -#26#>frac{1}{2} #31#>le c
#32#>le #33#>frac{1}{8}$$-12≤c≤18. This
bound is tight since for any $$k> #42#>frac{3n^2}{8}
-#47#>frac{n}{2}+#52#>frac{1}{8}$$k>3n28-n2+18there
exist bichromatic point sets that do not admit any perfect matching with k
crossings.