Intersecting k-Uniform Families Containing all the k-Subsets of a Given Set
نویسندگان
چکیده
Let m,n, and k be integers satisfying 0 < k 6 n < 2k 6 m. A family of sets F is called an (m,n, k)-intersecting family if ([n] k ) ⊆ F ⊆ ([m] k ) and any pair of members of F have nonempty intersection. Maximum (m, k, k)and (m, k + 1, k)-intersecting families are determined by the theorems of Erdős-KoRado and Hilton-Milner, respectively. We determine the maximum families for the cases n = 2k − 1, 2k − 2, 2k − 3, or m sufficiently large. Joint work with Bor-Liang Chen, Kuo-Ching Huang, and Ko-Wei Lih.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 20 شماره
صفحات -
تاریخ انتشار 2013