3-Wise Exactly 1-Intersecting Families of Sets
نویسنده
چکیده
Let f(l,t,n) be the maximal size of a family F ⊂ 2[n] such that any l ≥ 2 sets of F have an exactly t ≥ 1-element intersection. If l ≥ 3, it trivially comes from [8] that the optimal families are trivially intersecting (there is a t-element core contained by all the members of the family). Hence it is easy to determine f(l, t, n) = ⌊ l 2(n− 1) ⌋ +1. Let g(l, t, n) be the maximal size of an l-wise exaclty t-intersecting family that is not trivially t-intersecting. We give upper and lower bounds which only meet in the following case: g(3, 1, n) = n2/3(1 + o(1)). AMS classification: 05D05; 05B25
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عنوان ژورنال:
- Graphs and Combinatorics
دوره 21 شماره
صفحات -
تاریخ انتشار 2005