Rainbow factors in hypergraphs

TL;DR

This paper investigates the conditions under which a large hypergraph with bounded edge colouring contains a rainbow copy of a given hypergraph factor, establishing that the degree threshold matches that for uncoloured hypergraphs.

Contribution

It proves that the asymptotic degree threshold for rainbow $H$-factors in hypergraphs equals that for uncoloured hypergraphs, extending existing results to the rainbow setting.

Findings

Degree threshold for rainbow $H$-factors matches that for uncoloured hypergraphs.

Established asymptotic conditions for the existence of rainbow $H$-factors.

Results apply to hypergraphs with large minimum $ ext{ell}$-degree and bounded edge colourings.

Abstract

For any $r$-graph $H$, we consider the problem of finding a rainbow $H$-factor in an $r$-graph $G$ with large minimum $\ell$-degree and an edge-colouring that is suitably bounded. We show that the asymptotic degree threshold is the same as that for finding an $H$-factor.