Codegree Conditions for (Fractional) Steiner Triple Systems
Abstract
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.
Fields of Study & Subjects
graph theory and CDMA systems
Coding theory and cryptography
Wireless Communication Networks Research
Publication details
- Journal / source
- SIAM Journal on Discrete Mathematics
- Volume
- 40
- Issue
- 3
- Pages
- 959–987
- Publication date
- 3 July 2026
- Language
- EN