Spanning tight components in 4-uniform hypergraphs

TL;DR

This paper proves that in 4-uniform hypergraphs with a certain minimum codegree, there always exists a spanning tight component, confirming a specific conjecture for this case.

Contribution

It establishes the minimum codegree condition for spanning tight components in 4-uniform hypergraphs, settling a conjecture for this uniformity case.

Findings

Minimum codegree at least ⌊n/4⌋ guarantees a spanning tight component

The result is tight, meaning the bound cannot be improved

Settles the 4-uniform case of a broader conjecture

Abstract

We prove that every $n$-vertex 4-uniform hypergraph with minimum codegree at least $\lfloor n/4 \rfloor$ has a spanning tight component. This is tight, and it settles the 4-uniform case of a conjecture of Illingworth, Lang, M\"uyesser, Parczyk, and Sgueglia.