Maximum Size Intersecting Families Of Bounded Minimum Positive Co-Degree

Let H be an r-uniform hypergraph. The minimum positive co-degree of H, denoted by delta(+)(r-1)(H), is the minimum k such that if S is an (r - 1)-set contained in a hyperedge of H, then S is contained in at least k hyperedges of H. For r >= k fixed and n sufficiently large, we determine the maximum possible size of an intersecting r-uniform n-vertex hypergraph with minimum positive co-degree delta(+)(r-1) (H) >= k and characterize the unique hypergraph attaining this maximum. This generalizes the Erdos-Ko-Rado theorem which corresponds to the case k = 1. Our proof is based on the delta-system method.