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On Large Intersecting Subfamilies of Uniform Setfamilies by Richard A. Duke; Paul Erdős; Vojtěch Rödl is a Mathematics article available to read on EtoBox.

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## Abstract In an earlier work R. A. Duke and V. Rödl, The Erdős–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 < κ < 1/2, if __n__ is sufficiently large each family A of ⌊κ__n__⌋‐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__ = ⌊τ__n__⌋ for 0 < τ < κ. We show that for sufficiently large __n__ and __N__ each family of this type contains an __r__‐wise __t__‐intersecting subfamily of size at least __N__^1−δ^, and that, apart for the size of δ, this result is the best possible. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003

Who reads On Large Intersecting Subfamilies of Uniform Setfamilies?

Author

Richard A. Duke; Paul Erdős; Vojtěch Rödl

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 1042-9832)

Published

2003

Language

EN

Field

Mathematics (Physical Sciences)