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Halld\\'{o}rsson et al.\\ have shown that a graph is word-representable if and only if it admits a so-called semi-transitive orientation. A corollary to this result is that any 3-colorable graph is word-representable.\n  Akrobotu et al.\\ have shown that a triangulation of a grid graph is word-representable if and only if it is 3-colorable. 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Sun, Sergey Kitaev, Thomas Z.Q. Chen","submitted_at":"2015-07-24T05:45:16Z","abstract_excerpt":"A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\\neq y$, alternate in $w$ if and only if $(x,y)\\in E$. Halld\\'{o}rsson et al.\\ have shown that a graph is word-representable if and only if it admits a so-called semi-transitive orientation. A corollary to this result is that any 3-colorable graph is word-representable.\n  Akrobotu et al.\\ have shown that a triangulation of a grid graph is word-representable if and only if it is 3-colorable. 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