On maximum-sum matchings of points

Abstract

Huemer et al. (Discrete Math., 2019) proved that for any two point sets R and B with |R| = |B|, the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the matched pairs, has the property that all the disks induced by the matching have a common point. In this work we study the perfect matching that maximizes the total Euclidean distance. First, we prove that this setting does not always ensure the common intersection property of the disks. Second, we extend the study for sets of 2n uncolored points. As the main result, we prove that in this case all disks of the matching do have a common point.