  A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the
alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if
$(x,y)$ is an edge in $E$. Some graphs are word-representable, others are not.
It is known that a graph is word-representable if and only if it accepts a
so-called semi-transitive orientation.
  The main result of this paper is showing that a triangulation of any convex
polyomino is word-representable if and only if it is 3-colorable. We
demonstrate that this statement is not true for an arbitrary polyomino. We also
show that the graph obtained by replacing each $4$-cycle in a polyomino by the
complete graph $K_4$ is word-representable. We employ semi-transitive
orientations to obtain our results.
