Abstract. We establish an upper bound on the minimum codegree necessary for the existence of spanning, fractional Steiner triple systems in 3-uniform hypergraphs. This improves upon a result by Lee in 2023. In particular, together with results from Lee’s paper, our results imply that if Formula: see text is sufficiently large and satisfies some necessary divisibility conditions, then a 3-uniform, Formula: see text-vertex hypergraph Formula: see text contains a Steiner triple system if every pair of vertices forms an edge in Formula: see text with at least Formula: see text other vertices.
Michael Zheng (Fri,) studied this question.