Bulletin of the London Mathematical Society · 1994 · 56 citations · 0 references
Natural SciencesComputer ScienceMathematicsCombinatoricsDiscrete MathematicsSet TheoryCombinatorial Set TheoryConvex GeometryEnumerative CombinatoricsRamsey TheoryConvex SetsDisjoint SetsIntersecting FamiliesIntersection TheoremsRamsey IntersectionsRamsey's TheoremRamsey-type ArgumentsRamsey-type Theorems
Given a family of n convex compact sets in the plane, one can always choose n⅕ 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 nlog2/log5 ⩽n0·431.