论文信息 - A lower bound on the number of unit distances between the vertices of a convex polygon

A lower bound on the number of unit distances between the vertices of a convex polygon

Abstract This paper proves that for every n ⩾ 4 there is a convex n-gon such that the vertices of 2n − 7 vertex pairs are one unit of distance apart. This improves the previously best lower bound of ⌊ (5n − 5) 3 ⌋ given by Erdős and Moser if n ⩾ 17.

Herbert Edelsbrunner | Péter Hajnal | P. Hajnal | H. Edelsbrunner

[1] Zoltán Füredi,et al. The maximum number of unit distances in a convex n-gon , 1990, J. Comb. Theory, Ser. A.

[2] P. Erdös. On Sets of Distances of n Points , 1946 .

[3] E. Szemerédi,et al. Unit distances in the Euclidean plane , 1984 .