Article citationsMore>>

P. Erdös and G. Szekeres, “On Some Extremum Problems in Elementary Geometry,” Annales Universitatis Scientarium Budapestinensis de Rolando Eötvös Nominatae Sectio Mathematica, Vol. 3-4, No. 1, 1961, pp. 53-62. (Reprinted in: J. Spencer, Ed., Paul Erdös: The Art of Counting. Selected Writings, MIT Press, Cambridge, 1973, pp. 680-689.)

has been cited by the following article:

• TITLE: On Some Numbers Related to the Erdös-Szekeres Theorem

  AUTHORS: Mark J. Nielsen, William Webb

  KEYWORDS: Erdos-Szekeres Theorem; Combinatorial Geometry

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.3 No.3, July 12, 2013

  ABSTRACT: A crossing family of segments is a collection of segments each pair of which crosses. Given positive integers j and k,a(j,k) grid is the union of two pairwise-disjoint collections of segments (with j and k members, respectively) such that each segment in the first collection crosses all members of the other. Let c(k) be the least integer such that any planar set of c(k) points in general position generates a crossing family of k segments. Also let #(j,k) be the least integer such that any planar set of #(j,k) points in general position generates a (j,k)-grid. We establish here the facts 9≤c(3)≤16 and #(1,2)=8.