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- W2951646194 abstract "A collection of sets is {em intersecting} if every two members have nonempty intersection. We describe the structure of intersecting families of $r$-sets of an $n$-set whose size is quite a bit smaller than the maximum ${n-1 choose r-1}$ given by the ErdH os-Ko-Rado Theorem. In particular, this extends the Hilton-Milner theorem on nontrivial intersecting families and answers a recent question of Han and Kohayakawa for large $n$. In the case $r=3$ we describe the structure of all intersecting families with more than 10 edges. We also prove a stability result for the Erdos matching problem. Our short proofs are simple applications of the Delta-system method introduced and extensively used by Frankl since 1977." @default.
- W2951646194 created "2019-06-27" @default.
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- W2951646194 date "2016-02-03" @default.
- W2951646194 modified "2023-09-27" @default.
- W2951646194 title "The structure of large intersecting families" @default.
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