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(Discrete Mathematics, 2019) proved that for any two point sets <jats:italic>R<\/jats:italic> and <jats:italic>B<\/jats:italic> with <jats:inline-formula><jats:alternatives><jats:tex-math>$$|R|=|B|$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>|<\/mml:mo>\n                    <mml:mi>R<\/mml:mi>\n                    <mml:mo>|<\/mml:mo>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mo>|<\/mml:mo>\n                    <mml:mi>B<\/mml:mi>\n                    <mml:mo>|<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the perfect matching that matches points of <jats:italic>R<\/jats:italic> with points of <jats:italic>B<\/jats:italic>, and maximizes the total <jats:italic>squared<\/jats:italic> 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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$p\\in R$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>p<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mi>R<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$q\\in B$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>q<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mi>B<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> induces the disk of smallest diameter that covers <jats:italic>p<\/jats:italic> and <jats:italic>q<\/jats:italic>. Following this research line, in this paper we consider the perfect matching that maximizes the total Euclidean distance. First, we prove that this new matching for <jats:italic>R<\/jats:italic> and <jats:italic>B<\/jats:italic> does not always ensure the common intersection property of the disks. Second, we extend the study of this new matching for sets of 2<jats:italic>n<\/jats:italic> uncolored points in the plane, where a matching is just a partition of the points into <jats:italic>n<\/jats:italic> pairs. As the main result, we prove that in this case all disks of the matching do have a common point.\n<\/jats:p>","DOI":"10.1007\/s10898-022-01199-z","type":"journal-article","created":{"date-parts":[[2022,6,21]],"date-time":"2022-06-21T03:29:27Z","timestamp":1655782167000},"page":"111-128","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["On maximum-sum matchings of points"],"prefix":"10.1007","volume":"85","author":[{"given":"Sergey","family":"Bereg","sequence":"first","affiliation":[]},{"given":"Oscar P.","family":"Chac\u00f3n-Rivera","sequence":"additional","affiliation":[]},{"given":"David","family":"Flores-Pe\u00f1aloza","sequence":"additional","affiliation":[]},{"given":"Clemens","family":"Huemer","sequence":"additional","affiliation":[]},{"given":"Pablo","family":"P\u00e9rez-Lantero","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0095-1725","authenticated-orcid":false,"given":"Carlos","family":"Seara","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,21]]},"reference":[{"key":"1199_CR1","doi-asserted-by":"crossref","unstructured":"\u00c1brego, B.M., Arkin, E.M., Fern\u00e1ndez-Merchant, S., Hurtado, F., Kano, M., Mitchell, J.S.B., Urrutia, J.: Matching points with circles and squares. 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