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 -