Representations of families of triples over \(GF(2)\) (Q1812889)

Given a set \(\mathbf B\) of triples on the set \(\{1,2,\dots,n\}\), a family of subsets is called intersecting, if the intersection of any two members of that family contains at least one member of \(\mathbf B\). The paper shows, that the maximum size of such an intersecting family cannot exceed the obvious lower bound \(2^{n-3}\), if \(\mathbf B\) has the property, that no element belongs to more than 3 triples. This proves a conjecture of Chung et al. in the spacial case \(t=3\). The proof is given via a translation into colored hypergraphs.