In this paper we prove an optimal co-degrees resilience property for the binomial $k$-uniform hypergraph model $H_{n,p}^k$ with respect to perfect matchings. That is, for a sufficiently large $n$ which is divisible by $k$, and $p\geq C_k\log {n}/n$, we prove that with high probability every subgraph $H\subseteq H^k_{n,p}$ with minimum co-degree (meaning, the number of supersets every set of size $k-1$ is contained in) at least $(1/2+o(1))np$ contains a perfect matching.
@article{10_37236_8167,
author = {Asaf Ferber and Lior Hirschfeld},
title = {Co-degrees resilience for perfect matchings in random hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {1},
doi = {10.37236/8167},
zbl = {1437.05170},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8167/}
}
TY - JOUR
AU - Asaf Ferber
AU - Lior Hirschfeld
TI - Co-degrees resilience for perfect matchings in random hypergraphs
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/8167/
DO - 10.37236/8167
ID - 10_37236_8167
ER -
%0 Journal Article
%A Asaf Ferber
%A Lior Hirschfeld
%T Co-degrees resilience for perfect matchings in random hypergraphs
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8167/
%R 10.37236/8167
%F 10_37236_8167
Asaf Ferber; Lior Hirschfeld. Co-degrees resilience for perfect matchings in random hypergraphs. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8167
