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- W2395767617 abstract "Let ℱ be a family ofk-subsets of ann-set. Lets be a fixed integer satisfyingk≦s≦3k. Suppose that forF 1,F 2,F 3 ∈ ℱ |F 1 ∪F 2 ∪F 3|≦s impliesF 1 ∩F 2 ∩F 3 ≠ 0. Katona asked what is the maximum cardinality,f(n, k, s) of such a system. The Erdős-Ko-Rado theorem impliesf(n, k, s)= $$left( {_{k - 1}^{n - 1} } right)$$ fors=3k andn≧2k. In this paper we show thatf(n, k, s)= $$left( {_{k - 1}^{n - 1} } right)$$ holds forn>n 0(k) if and only ifs≧2k. Equality holds only if every member of ℱ contains a fixed element of the underlying set. Further we solve the problem fork=3,s=5,n≧3000. This result sharpens a theorem of Bollobás." @default.
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- W2395767617 date "1983-09-01" @default.
- W2395767617 modified "2023-10-01" @default.
- W2395767617 title "A new generalization of the Erdős-Ko-Rado theorem" @default.
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- W2395767617 doi "https://doi.org/10.1007/bf02579190" @default.
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