THE ERDOS-SZEKERES PROBLEM FOR NON-CROSSING CONVEX SETS

Cited 3 time in webofscience Cited 0 time in scopus
  • Hit : 323
  • Download : 0
We show an equivalence between a conjecture of Bisztriczky and Fejes T ' oth about families of planar convex bodies and a conjecture of Goodman and Pollack about point sets in topological affine planes. As a corollary of this equivalence we improve the upper bound of Pach and T ' oth on the Erdos-Szekeres theorem for disjoint convex bodies, as well as the recent upper bound obtained by Fox, Pach, Sudakov and Suk on the Erdos-Szekeres theorem for non-crossing convex bodies. Our methods also imply improvements on the positive fraction Erdos-Szekeres theorem for disjoint (and non-crossing) convex bodies, as well as a generalization of the partitioned Erd " os-Szekeres theorem of P or and Valtr to families of non-crossing convex bodies.
Publisher
LONDON MATH SOC
Issue Date
2014-07
Language
English
Article Type
Article
Keywords

THEOREM; CONFIGURATIONS; BODIES; ARRANGEMENTS; POSITION; PLANES

Citation

MATHEMATIKA, v.60, no.2, pp.463 - 484

ISSN
0025-5793
DOI
10.1112/S0025579314000072
URI
http://hdl.handle.net/10203/190051
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 3 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0