An Extremal Set-Intersection Theorem
Vašek Chvátal · Journal of the London Mathematical Society · 1974
Let S be a set with n elements and Fa set of k-point subsets of S, n ⩾ k + 1 ⩾ 5. If |F|> ( n − 1 k − 1 ) then there is a subset G= {Xl, X2, .., Xk} of F such that, for each i, all the k−1 sets in G—{X1} have at least one element in common but all the k sets in G have no element in common.