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3-Wise Exactly 1-Intersecting Families of Sets
<span title="">2005</span>
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<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yxooi3wjmbgqtbp7l4evjeuj4i" style="color: black;">Graphs and Combinatorics</a>
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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
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... hich only meet in the following case: g(3, 1, n) = n 2/3 (1 + o(1)).
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