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arXiv · 2608.21347

Exact Minimum $d$-Degree Thresholds for Hypergraph Perfect Matchings

Jie Han·Hongliang Lu·Bin Wang·Feihong Yuan
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Abstract

For fixed integers $k\ge3$ and $1\le d\le k-1$ and sufficiently large $n\in k\mathbb N$, we establish the sharp minimum $d$-degree thresholds that forces perfect matching in every $n$-vertex $k$-uniform hypergraphs. This was conjectued by Treglown and Zhao, and the $d=1$ case was conjectued by Kühn, Osthus and Treglown.

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Jie Han, Hongliang Lu, Bin Wang, Feihong Yuan. 2026-08-21. Exact Minimum $d$-Degree Thresholds for Hypergraph Perfect Matchings. https://arxiv.org/abs/2608.21347

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