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A Ramsey‐Type Result for Convex Sets
Author(s) -
Larman David,
Matoušek Jiří,
Pach János,
Törőcsik Jenő
Publication year - 1994
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/26.2.132
Subject(s) - pairwise comparison , mathematics , disjoint sets , combinatorics , regular polygon , plane (geometry) , subfamily , type (biology) , discrete mathematics , geometry , statistics , ecology , biochemistry , chemistry , biology , gene
Given a family of n convex compact sets in the plane, one can always choose n ⅕ of them which are either pairwise disjoint or pairwise intersecting. On the other hand, there exists a family of n segments in the plane such that the maximum size of a subfamily with pairwise disjoint or pairwise intersecting elements in n log2/log5 ⩽ n 0·431 .
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