I would like to know if there exists a version of König's theorem for tripartite $3$-graphs.

In other words, let $G = (V,T)$ be a tripartite $3$-graph. That is, $V$ is a set of vertices (with $V$ equal to the union of three disjoint subsets $A,B,C$) and $T$ is a set of hyperedges $\{v_1,v_2,v_3\}$, with $v_1 \in A, v_2 \in B, v_3 \in C$. A *matching* is a collection of hyperedges such that no two of them share a vertex. A *cover* is a set of vertices that meets every hyperedge.

Is there a relationship between the size of a maximum matching and the size of a minimum cover in $G$.

Any suggestions or references? Thanks in advance!