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arXiv · 2411.07981

Codegree conditions for (fractional) Steiner triple systems

Michael Zheng
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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 $n$ 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.

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Michael Zheng. 2026-02-12. Codegree conditions for (fractional) Steiner triple systems. https://arxiv.org/abs/2411.07981

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