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A comprehensive introduction to the theory of word-representable graphs

Kitaev, Sergey (2017) A comprehensive introduction to the theory of word-representable graphs. In: Developments in Language Theory. Lecture Notes in Computer Science . Springer-Verlag, Berlin. (In Press)

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Abstract

Letters x and y alternate in a word w if after deleting in w all letters but the copies of x and y we either obtain a word xyxy⋯ (of even or odd length) or a word yxyx⋯  (of even or odd length). A graph G=(V,E) is word-representable if and only if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if xy ∈ E.   Word-representable graphs generalize several important classes of graphs such as circle graphs, 3-colorable graphs and comparability graphs. This paper offers a comprehensive introduction to the theory of word-representable graphs including the most recent developments in the area.