Word-representability of triangulations of rectangular polyomino with a single domino tile

Abstract

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

To appear in the Journal of Combinatorial Mathematics and Combinatorial Computing