A Generalization of the Erdos - Szekeres Theorem to Disjoint Convex Sets

@article{Pach1998AGO,
  title={A Generalization of the Erdos - Szekeres Theorem to Disjoint Convex Sets},
  author={J{\'a}nos Pach and G{\'e}za T{\'o}th},
  journal={Discrete & Computational Geometry},
  year={1998},
  volume={19},
  pages={437-445}
}
Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex position, if none of its members is contained in the convex hull of the union of the others. For any xed k 3, we estimate P k (n), the maximum size of a family F with the property that any k members of F are in convex position, but no n are. In particular, for k = 3, we improve the triply exponential upper bound of T. Bisztriczky and G. Fejes TT oth by showing that P 3 (n) < 16 n . 

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-6 of 6 references

Recent progress on packing and covering, in: Proceedings of Conference on Discrete and Computational Geometry: Ten Years Later (Mount Holyoke

  • G Fejes, Tt Oth
  • Contemporary Mathematics
  • 1996

A generalization of the Erd} os-Szekeres convex n-gon theorem

  • Bf, T Bisztriczky, G Fejes, Tt Oth
  • Journal f ur die reine und angewandte Mathematik
  • 1989

Komll os, Some combinatorial theorems on monotonicity

  • Ck, V Chvv
  • Canad. Math. Bull
  • 1971

A combinatorial problem in geometry

  • Es, P Erd} Os, G Szekeres
  • Compositio Mathematica
  • 1935

Similar Papers

Loading similar papers…