A proof of the Elliott-Rödl conjecture on hypertrees in Steiner triple systems

Seonghyuk Im; Jaehoon Kim; Joonkyung Lee; Abhishek Methuku

doi:10.1017/fms.2024.34

A proof of the Elliott-Rödl conjecture on hypertrees in Steiner triple systems

Seonghyuk Im, Jaehoon Kim, Joonkyung Lee, Abhishek Methuku

Research output: Contribution to journal › Article › peer-review

Abstract

Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and Rödl conjectured that for any given 0$ ]]>, there exists such that the following holds. Every n-vertex Steiner triple system contains all hypertrees with at most vertices whenever. We prove this conjecture.

Original language	English (US)
Article number	e75
Journal	Forum of Mathematics, Sigma
Volume	12
Early online date	Sep 6 2024
DOIs	https://doi.org/10.1017/fms.2024.34
State	Published - Sep 6 2024
Externally published	Yes

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1017/fms.2024.34

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abstract = "Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and R{\"o}dl conjectured that for any given 0$ ]]>, there exists such that the following holds. Every n-vertex Steiner triple system contains all hypertrees with at most vertices whenever. We prove this conjecture.",

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A proof of the Elliott-Rödl conjecture on hypertrees in Steiner triple systems

Abstract

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