We determine the minimum degree sum of two adjacent vertices that ensures a perfect matching in a 3-uniform hypergraph without an isolated vertex. Suppose that $H$ is a 3-uniform hypergraph whose order $n$ is sufficiently large and divisible by $3$. If $H$ contains no isolated vertex and $\deg(u)+\deg(v) > \frac{2}{3}n^2-\frac{8}{3}n+2$ for any two vertices $u$ and $v$ that are contained in some edge of $H$, then $H$ contains a perfect matching. This bound is tight and the (unique) extremal hyergraph is a different space barrier from the one for the corresponding Dirac problem.
@article{10_37236_7658,
author = {Yi Zhang and Yi Zhao and Mei Lu},
title = {Vertex degree sums for perfect matchings in 3-uniform hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {3},
doi = {10.37236/7658},
zbl = {1395.05136},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7658/}
}
TY - JOUR
AU - Yi Zhang
AU - Yi Zhao
AU - Mei Lu
TI - Vertex degree sums for perfect matchings in 3-uniform hypergraphs
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/7658/
DO - 10.37236/7658
ID - 10_37236_7658
ER -
%0 Journal Article
%A Yi Zhang
%A Yi Zhao
%A Mei Lu
%T Vertex degree sums for perfect matchings in 3-uniform hypergraphs
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/7658/
%R 10.37236/7658
%F 10_37236_7658
Yi Zhang; Yi Zhao; Mei Lu. Vertex degree sums for perfect matchings in 3-uniform hypergraphs. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7658
