An Improvement of the Lower Bound on the Minimum Number of ? k -Edges

Javier Rodrigo, Susana Merchán, Danilo Magistrali and Mariló López
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Javier Rodrigo: Departamento de Matemática Aplicada, E.T.S.I. Universidad Pontificia Comillas, Alberto Aguilera 25, 28015 Madrid, Spain
Susana Merchán: Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Escuela de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Profesor Aranguren, 3, 28040 Madrid, Spain
Danilo Magistrali: Departamento de Matemática Aplicada, E.T.S.I. Universidad Pontificia Comillas, Alberto Aguilera 25, 28015 Madrid, Spain
Mariló López: Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Escuela de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Profesor Aranguren, 3, 28040 Madrid, Spain

Mathematics, 2021, vol. 9, issue 5, 1-9

Abstract: In this paper, we improve the lower bound on the minimum number of ? k -edges in sets of n points in general position in the plane when k is close to n 2 . As a consequence, we improve the current best lower bound of the rectilinear crossing number of the complete graph K n for some values of n .

Keywords: combinatorial geometry; ?k-edges; rectilinear crossing number; optimization; complete graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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