Download PDFOpen PDF in browserOn MaximumSum Matchings of PointsEasyChair Preprint no. 603817 pages•Date: July 9, 2021AbstractHuemer et al. (Discrete Mathematics, 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. Each pair of matched points p in R and q in B induces the disk of smallest diameter that covers p and q. Following this research line, in this article we consider the perfect matching that maximizes the total Euclidean distance. First, we prove that this new matching for R and B does not always ensure the common intersection property of the disks. Second, we extend the study of this new matching for sets of 2n uncolored points in the plane, where a matching is just a partition of the points into n pairs. As the main result, we prove that in this case all disks of the matching do have a common point. Keyphrases: Colored points, Disks, intersection graph, matchings, Maxsum Euclidean matching
