On large intersecting subfamilies of uniform setfamilies

Authors:
Richard A. Duke;Paul Erdős;Vojtěch Rödl
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia;Hungarian Academy of Sciences, Budapest, Hungary;Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia
Venue:
Random Structures & Algorithms
Year:
2003

Citing 4
Cited 1

Cycle-connected graphs

Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
The Erdős-Ko-Rado theorem for small families

Journal of Combinatorial Theory Series A
The complete intersection theorem for systems of finite sets

European Journal of Combinatorics
On graphs with small Ramsey numbers

Journal of Graph Theory

On a problem of Duke--Erdős--Rödl on cycle-connected subgraphs

Journal of Combinatorial Theory Series B

Quantified Score

Hi-index	0.00

Visualization

Abstract

In an earlier work [R. A. Duke and V. Rödl, The Erdös-Ko-Rado theorem for small families, J Combin Theory Ser A 65(2) (1994), 246-251] it was shown that for t a fixed positive integer and κ a real constant, 0 n is sufficiently large each family A of ⌊κn⌋-element subsets of [n] of size N (linear in n) contains a t-intersecting subfamily of size at least (1 - o(1)) κ N. Here we consider the case when t, the intersection size, is no longer bounded, specifically t = ⌊τn⌋ for 0 n and N each family of this type contains an r-wise t-intersecting subfamily of size at least N1-γ, and that, apart for the size of γ this result is the best possible.