Vertex Degree Sums for Matchings in 3-Uniform Hypergraphs

• DOI: 10.37236/8627
• Publication Date: 2020-01-10T06:04:34Z
• Authors: Yi Zhang; Yi Zhao; Mei Lu
• Keywords: Hypergraph; Degree (music)

Let $n, s$ be positive integers such that $n$ is sufficiently large and $s\le n/3$. Suppose $H$ a 3-uniform hypergraph of order without isolated vertices. If $\deg(u)+\deg(v) > 2(s-1)(n-1)$ for any two vertices $u$ $v$ are contained in some edge $H$, then contains matching size $s$. This degree sum condition best possible confirms conjecture the authors [Electron. J. Combin. 25 (3), 2018], who proved case when $s=