We determine the exact minimum $\ell$-degree threshold for perfect matchings in $k$-uniform hypergraphs when the corresponding threshold for perfect fractional matchings is significantly less than $\frac{1}{2}\left( \begin{array}{c} n \\ k- \ell\end{array}\right)$. This extends our previous results that determine the minimum $\ell$-degree thresholds for perfect matchings in $k$-uniform hypergraphs for all $\ell\ge k/2$ and provides two new (exact) thresholds: $(k,\ell)=(5,2)$ and $(7,3)$.
@article{10_37236_5406,
author = {Andrew Treglown and Yi Zhao},
title = {A note on perfect matchings in uniform hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {1},
doi = {10.37236/5406},
zbl = {1329.05247},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5406/}
}
TY - JOUR
AU - Andrew Treglown
AU - Yi Zhao
TI - A note on perfect matchings in uniform hypergraphs
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/5406/
DO - 10.37236/5406
ID - 10_37236_5406
ER -
%0 Journal Article
%A Andrew Treglown
%A Yi Zhao
%T A note on perfect matchings in uniform hypergraphs
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/5406/
%R 10.37236/5406
%F 10_37236_5406
Andrew Treglown; Yi Zhao. A note on perfect matchings in uniform hypergraphs. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/5406
