A RAMSEY-TYPE RESULT FOR CONVEX-SETS

Authors
LARMAN D MATOUSEK J PACH J TOROCSIK J
Citation
D. Larman et al., A RAMSEY-TYPE RESULT FOR CONVEX-SETS, Bulletin of the London Mathematical Society, 26, 1994, pp. 132-136
Citations number
12
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Bulletin of the London Mathematical Society → ACNP
ISSN journal
00246093
Volume
26
Year of publication
1994
Part
2
Pages
132 - 136
Database
ISI
SICI code
0024-6093(1994)26:<132:ARRFC>2.0.ZU;2-X
Abstract
Given a family of n convex compact sets in the plane, one can always c hoose n1/5 of them which are either pairwise disjoint or pairwise inte rsecting. On the other hand, there exists a family of n segments in th e plane such that the maximum size of a subfamily with pairwise disjoi nt or pairwise intersecting elements in n(log2/log5) less-than-or-equa l-to 0.431.