The maximum number of halving lines and the rectilinear crossing number of Kn for n

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}.

• Type: Journal
• Year: 2008
• Where: ENDM
• Authors: Bernardo M. Ábrego, Silvia Fernández-Merchant, Jesús Leaños, Gelasio Salazar
• Keywords: ENDM 2008, Exact Values, Halving, Maximum Number