# Co-degrees resilience for perfect matchings in random hypergraphs

## TL;DR

This paper establishes an optimal co-degrees resilience property in random hypergraphs, showing that with high probability, subgraphs with sufficiently high co-degree contain perfect matchings.

## Contribution

It proves a new resilience threshold for perfect matchings in binomial random hypergraphs, extending understanding of hypergraph matchings under adversarial conditions.

## Key findings

- High probability subgraphs with minimum co-degree above half the expected degree contain perfect matchings.
- The result is optimal up to lower order terms, matching known thresholds.
- The proof applies probabilistic and combinatorial techniques to hypergraph resilience.

## Abstract

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.