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- W2950016669 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 $E$. Some graphs are word-representable, others are not. It is known that a graph is word-representable if and only if it accepts a so-called semi-transitive orientation. The main result of this paper is showing that a triangulation of any convex polyomino is word-representable if and only if it is 3-colorable. We demonstrate that this statement is not true for an arbitrary polyomino. We also show that the graph obtained by replacing each $4$-cycle in a polyomino by the complete graph $K_4$ is word-representable. We employ semi-transitive orientations to obtain our results." @default.
- W2950016669 created "2019-06-27" @default.
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- W2950016669 date "2014-05-14" @default.
- W2950016669 modified "2023-09-27" @default.
- W2950016669 title "On word-representability of polyomino triangulations" @default.
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