Almost perfect matchings in $k$-partite $k$-graphs

Abstract

The minimum co-degree threshold for a perfect matching in a $k$-graph with $n$ vertices was determined by Rödl, Ruciński and Szemerédi for the case when $n\equiv 0\pmod k$. Recently, Han resolved the remaining cases when $n \not\equiv 0\pmod k$, establishing a conjecture of Rödl, Ruciński and Szemerédi. In this paper, we determine the minimum co-degree threshold for almost perfect matchings in $k$-partite $k$-graphs, answering a question of Rödl and Ruciński.