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Графы, представимые в виде слов : обзор результатов

Kitaev, Sergey and Pyatkin, Artem (2018) Графы, представимые в виде слов : обзор результатов. Diskretnyi Analiz i Issledovanie Operatsii, 25 (2). pp. 19-53. ISSN 1990-4797

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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 is a comprehensive survey on the theory of word-representable graphs and it includes the most recent developments in the area.