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

Glen, Marc and Kitaev, Sergey (2015) Word-representability of triangulations of rectangular polyomino with a single domino tile. Journal of Combinatorial Mathematics and Combinatorial Computing. (In Press)

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Abstract

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 1x1 tiles on a rectangular polyomino.