Abstract
Recall that, by Theorem 3.4.3, a graph is permutationally representable if and only if it is a comparability graph. The current chapter offers, based on [74, 75], a generalization of this theorem to the case of arbitrary word-representable graphs and so-called semi-transitive orientations (see Theorem 4.1.8). These acyclic orientations, being a generalization of transitive orientations related to partial orders, provide a powerful tool for studying word-representable graphs, in particular, allowing us to reformulate word-representability problems in pure graph-theoretical terms (via certain orientations of graphs).
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© 2015 Springer International Publishing Switzerland
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Kitaev, S., Lozin, V. (2015). Characterization of Word-Representable Graphs in Terms of Semi-transitive Orientations. In: Words and Graphs. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Cham. https://doi.org/10.1007/978-3-319-25859-1_4
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DOI: https://doi.org/10.1007/978-3-319-25859-1_4
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-25859-1
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