Geodesic
A proof of the Elliott–Rödl conjecture on hypertrees in Steiner triple systems
Forum of Mathematics, Sigma, Tome 12 (2024)

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Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and Rödl conjectured that for any given $\mu>0$, there exists $n_0$ such that the following holds. Every n-vertex Steiner triple system contains all hypertrees with at most $(1-\mu )n$ vertices whenever $n\geq n_0$. We prove this conjecture. 
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     title = {A proof of the {Elliott{\textendash}R\"odl} conjecture on hypertrees in {Steiner} triple systems},
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Seonghyuk Im; Jaehoon Kim; Joonkyung Lee; Abhishek Methuku. A proof of the Elliott–Rödl conjecture on hypertrees in Steiner triple systems. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.34

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