Let $n, s$ be positive integers such that $n$ is sufficiently large and $s\le n/3$. Suppose $H$ is a 3-uniform hypergraph of order $n$ without isolated vertices. If $\deg(u)+\deg(v) > 2(s-1)(n-1)$ for any two vertices $u$ and $v$ that are contained in some edge of $H$, then $H$ contains a matching of size $s$. This degree sum condition is best possible and confirms a conjecture of the authors [Electron. J. Combin. 25 (3), 2018], who proved the case when $s= n/3$.
@article{10_37236_8627,
author = {Yi Zhang and Yi Zhao and Mei Lu},
title = {Vertex degree sums for matchings in 3-uniform hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/8627},
zbl = {1422.05088},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8627/}
}
TY - JOUR
AU - Yi Zhang
AU - Yi Zhao
AU - Mei Lu
TI - Vertex degree sums for matchings in 3-uniform hypergraphs
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8627/
DO - 10.37236/8627
ID - 10_37236_8627
ER -
%0 Journal Article
%A Yi Zhang
%A Yi Zhao
%A Mei Lu
%T Vertex degree sums for matchings in 3-uniform hypergraphs
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8627/
%R 10.37236/8627
%F 10_37236_8627
Yi Zhang; Yi Zhao; Mei Lu. Vertex degree sums for matchings in 3-uniform hypergraphs. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/8627
