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A proof of the Elliott-Rödl conjecture on hypertrees in Steiner triple systems
- Publication Year :
- 2022
- Publisher :
- arXiv, 2022.
-
Abstract
- Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and Rödl conjectured that for any given $μ>0$, there exists $n_0$ such that the following holds. Every $n$-vertex Steiner triple system contains all hypertrees with at most $(1-μ)n$ vertices whenever $n\geq n_0$. We prove this conjecture.<br />19 pages, 2 figures
- Subjects :
- FOS: Mathematics
Combinatorics (math.CO)
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi...........a2811880269d41c8186398d43e8722ae
- Full Text :
- https://doi.org/10.48550/arxiv.2208.10370