2024/11/12 by Zheng, Michael
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2411.07981
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 n is sufficiently large and satisfies some necessary divisibility conditions, then a 3-uniform, n-vertex hypergraph H contains a Steiner triple system if every pair of vertices forms an edge in H with at least 0.8579n other vertices.