%0 Journal Article
%T The number of non-crossing perfect plane matchings is minimized (almost) only by point sets in convex position
%A Andrei Asinowski
%J Computer Science
%D 2015
%I arXiv
%X It is well-known that the number of non-crossing perfect matchings of $2k$ points in convex position in the plane is $C_k$, the $k$th Catalan number. Garc\'ia, Noy, and Tejel proved in 2000 that for any set of $2k$ points in general position, the number of such matchings is at least $C_k$. We show that the equality holds only for sets of points in convex position, and for one exceptional configuration of $6$ points.
%U http://arxiv.org/abs/1502.05332v1