TY - JOUR

T1 - Word-representability of triangulations of rectangular polyomino with a single domino tile

AU - Glen, Marc

AU - Kitaev, Sergey

PY - 2015/9/9

Y1 - 2015/9/9

N2 - 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.

AB - 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.

KW - word-representability

KW - polyomino

KW - triangulation

KW - domino

UR - http://www.combinatorialmath.ca/jcmcc/toc.html

UR - http://arxiv.org/abs/1503.05076

M3 - Article

JO - Journal of Combinatorial Mathematics and Combinatorial Computing

JF - Journal of Combinatorial Mathematics and Combinatorial Computing

SN - 0835-3026

ER -