This is a special case of Ryser's Conjecture, which states that in an $r$-partite, $r$-uniform hypergraph (with $r>1$)

$\tau \leq (r-1) \nu$,

where $\tau$ is the size of a minimum cover and $\nu$ is the size of a maximum matching. Note that the case $r=2$ is simply König's theorem.

You are interested in the case $r=3$, which was settled by Aharoni. The reference is

Ron Ryser's conjecture for tripartite 3-graphs. Combinatorica 21 (2001), no. 1, 1--4,

and you can find a copy of the paper here.

This is a special case of Ryser's Conjecture, which states that in an $r$-partite, $r$-uniform hypergraph (with $r>1$)

$\tau \leq (r-1) \nu$,

where $\tau$ is the size of a minimum cover and $\nu$ is the size of a maximum matching. Note that the case $r=2$ is simply König's theorem.

You are interested in the case $r=3$, which was settled by Aharoni. The reference is

Ryser's conjecture for tripartite 3-graphs. Combinatorica 21 (2001), no. 1, 1--4,

and you can find a copy of the paper here.

Check out Ryser's conjecture here. It looks like you are interested in the case r=3 (3-uniform, 3-partite hypergraphs), which was recently settled by Aharoni. The reference is

Ron Ryser's conjecture for tripartite 3-graphs. Combinatorica 21 (2001), no. 1, 1--4.

This is a special case of Ryser's Conjecture, which states that in an $r$-partite, $r$-uniform hypergraph (with $r>1$)

$\tau \leq (r-1) \nu$,

where $\tau$ is the size of a minimum cover and $\nu$ is the size of a maximum matching. Note that the case $r=2$ is simply König's theorem.

You are interested in the case $r=3$, which was settled by Aharoni. The reference is

Ron Ryser's conjecture for tripartite 3-graphs. Combinatorica 21 (2001), no. 1, 1--4,

and you can find a copy of the paper here.