An Improvement of the Lower Bound on the Minimum Number of ≤k-Edges - Javier Rodrigo; Susana Merchán; Danilo Magistrali; Mariló López (Mathematics, 2021)
In this paper, we improve the lower bound on the minimum number of <semantics> ≤k</semantics>-edges in sets of n points in general position in the plane when k is close to <semantics>n2</semantics>. As a consequence, we improve the current best lower bound of the rectilinear crossing number of the complete graph <semantics>Kn</semantics> for some values of n.