Piercing Families of Convex Sets with the d-Intersection Property in ℝ d
- 70 Downloads
In this paper, we consider finite families of convex sets in ℝ d such that every d or fewer sets of the family have a common point. For some families of this type, we give upper bounds on the size of a finite set intersecting all sets of the family.
KeywordsPiercing Helly’s theorem Transversal
- 1.Danzer, L., Grünbaum, B., Klee, V.: Helly’s theorem and its relatives. In: Convexity, Proc. of Symposia in Pure Math., vol. 7, pp. 101–180. Am. Math. Soc., Providence (1963) Google Scholar
- 2.Eckhoff, J.: Helly, Radon, and Carathéodory type theorems. In: Gruber, P.M., Willis, J.M. (eds.) Handbook of Convex Geometry, pp. 389–448. North-Holland, Amsterdam (1993) Google Scholar