# Are all polyominoes with even sides tileable by dominoes?

In this paper (Section 8) the author states that it is "trivial" to show that a polyomino with all sides (including the sides of holes in the polyomino) even has a tiling by dominoes.

It is indeed easy to see for polyominoes without holes, but the general case does not seem so obvious to me. One thing that makes it tricky is that the holes can appear anywhere as long as their borders do not overlap or coincide. (This makes it difficult to find a proof that reduces the figure but keeps the even-sides constraint.)

Is there indeed a trivial proof for this?

Note: I asked a earlier question about what the same author calls "even" polyominoes, but those polyominoes are completely different.

Update: The proof also works for figures with sides divisible by $$n$$ and bars of length $$n$$ instead of dominoes if the holes are at least $$n - 1$$ units apart. I think (but am not sure) that we can remove this constraint if the tile set is all $$n$$-ominoes.