An extension of the Erdős–Ko–Rado Theorem

A family G⊂2[n] is called r-wise t-intersecting if |G1∩⋯∩Gr|⩾t holds for all G1,…,Gr∈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 for r⩾7, 1⩽t⩽r2−r−1 and k>k0(r).