Larger matchings and independent sets in regular uniform hypergraphs of high girth

TL;DR

This paper analyzes algorithms for matchings and independent sets in large girth, regular hypergraphs, providing new lower bounds on their maximum sizes, advancing understanding of hypergraph combinatorics.

Contribution

It introduces and analyzes algorithms for matchings and independent sets in high-girth, regular hypergraphs, establishing new bounds on their sizes.

Findings

New lower bounds for maximum matchings in hypergraphs.

New lower bounds for maximum independent sets in hypergraphs.

Algorithms effective in high-girth, regular hypergraph settings.

Abstract

In this note we analyze two algorithms, one for producing a matching and one for an independent set, on $k$-uniform $d$-regular hypergraphs of large girth. As a result we obtain new lower bounds on the size of a maximum matching or independent set in such hypergraphs.