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

Hongliang Lu, Yan Wang, Xingxing Yu

Published 2016-08-17Version 1

The minimum co-degree threshold for a perfect matching in a $k$-graph with $n$ vertices was determined by R\"odl, Ruci\'nski and Szemer\'edi for the case when $n\equiv 0\pmod k$. Recently, Han resolved the remaining cases, establishing a conjecture of R\"odl, Ruci\'nski and Szemer\'edi. In this paper, we determine the minimum co-degree threshold for almost perfect matchings in $k$-partite $k$-graphs, answering a question of R\"odl and Ruci\'nski.