An extension of the Erdős–Ko–Rado Theorem

A family G ⊂ 2 [ n ] is called r-wise t-intersecting if | G 1 ∩ ⋯ ∩ G r | ⩾ t holds for all G 1 , … , G r ∈ G . We report some results concerning the maximum size of r-wise t-intersecting families with additional conditions. For example, any k-uniform r-wise t-intersecting family on 2k vertices has size at most ( 2 k − 1 k − 1 ) for r ⩾ 7 , 1 ⩽ t ⩽ 2 r − r − 1 and k > k 0 ( r ) .