On the chromatic number of random regular hypergraphs

TL;DR

This paper investigates the typical chromatic and independence numbers of large random regular hypergraphs, providing estimations for fixed uniformity and large degree as the number of vertices grows.

Contribution

It offers new estimations for the chromatic and independence numbers of random regular hypergraphs with fixed uniformity and large degree.

Findings

Estimated values of chromatic numbers for large hypergraphs.

Estimated independence numbers for large hypergraphs.

Results applicable to fixed uniformity and large degree regimes.

Abstract

We estimate the likely values of the chromatic and independence numbers of the random $r$-uniform $d$-regular hypergraph on $n$ vertices for fixed $r$, large fixed $d$, and $n \rightarrow \infty$.