An Improvement of the Upper Bound for the Number of Halving Lines of Planar Sets
Estrella Alonso,
Mariló López,
Javier Rodrigo
Affiliations
Estrella Alonso
Department of Applied Mathematics, Technical School of Engineering, Comillas Pontifical University, Calle de Alberto Aguilera 25, 28015 Madrid, Spain
Mariló López
Department of Mathematics and Computer Science Applied to Civil Engineering, Polytechnic University of Madrid, Calle del Profesor Aranguren 3, 28040 Madrid, Spain
Javier Rodrigo
Department of Applied Mathematics, Technical School of Engineering, Comillas Pontifical University, Calle de Alberto Aguilera 25, 28015 Madrid, Spain
In this paper, we provide improvements in the additive constant of the current best asymptotic upper bound for the maximum number of halving lines for planar sets of n points, where n is an even number. We also improve this current best upper bound for small values of n, namely, 106≤n≤336. To obtain this enhancements, we provide lower bounds for the sum of the squares of the degrees of the vertices of a graph related to the halving lines.
