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.Comment: To appear in the Journal of Combinatorial Mathematics and
  Combinatorial Computin

Glen, Marc

Kitaev, Sergey

English

arXiv

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

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

University of Strathclyde Institutional Repository

http://strathprints.strath.ac.uk/54275/1/Glen_Kitaev_JCMCC2015_word_representability_of_triangulations_of_rectangular_polyomino.pdf

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

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University of Strathclyde Institutional Repository