Partitioning infinite hypergraphs into few monochromatic Berge-paths

Abstract

Extending a result of Rado to hypergraphs, we prove that for all $s,k,t\in \mathbb{N}$ with $k\ge t\ge 2$, the vertices of every $r=s(k-t+1)$-edge-coloured countably infinite complete $k$-graph can be partitioned into the cores of at most $s$ monochromatic $t$-tight Berge-paths of different colours. We further describe a construction showing that this result is best possible.