 
Summary: The maximum number of halving lines and the
rectilinear crossing number of Kn for n 27
Bernardo M. ´Abrego
Silvia Fern´andezMerchant
Department of Mathematics, California State University at Northridge
Jes´us Lea~nos
Gelasio Salazar
Instituto de F´isica, Universidad Aut´onoma de San Luis Potos´i, M´exico
Abstract
For n 27 we present exact values for the maximum number h(n) of halving
lines and h(n) of halving pseudolines, determined by n points in the plane. For
this range of values of n we also present exact values of the rectilinear cr(Kn)
and the pseudolinear cr(Kn) crossing numbers of the complete graph Kn. h(n)
and cr(Kn) are new for n {14, 16, 18, 20, 22, 23, 24, 25, 26, 27}, h(n) is new for n
{16, 18, 20, 22, 23, 24, 25, 26, 27}, and cr(Kn) is new for n {20, 22, 23, 24, 25, 26, 27}.
Keywords: Halving lines, rectilinear crossing number, complete graphs
1 Introduction
Let S be an npoint set in R2
in general position. A kset of S is a set P
of k points in S that can be separated from S\P using a straight line. The
