Word-Representability of Triangulations of Rectangular Polyomino with a Single Domino Tile

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 \( E \).

A recent elegant result of Akrobotu \( et \, al. \) \([1]\) states that a triangulation of any convex polyomino is word-representable if and only if it is 3-colourable. In this paper, we generalize a particular case of this result by showing that the result of Akrobotu \( et \, al. \) \([1]\) is true even if we allow a domino tile, instead of having just \(1 \times 1\) tiles on a rectangular polyomino.