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Word-Representable Graphs: a Survey

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Abstract

Letters x and y alternate in a word w if after deleting all letters but x and y in w we get either a word xyxy... or a word yxyx... (each of these words can be of odd or even length). A graph G = (V,E) is word-representable if there is a finite word w over an alphabet V such that the letters x and y alternate in w if and only if xy ∈ E. The word-representable graphs include many important graph classes, in particular, circle graphs, 3-colorable graphs and comparability graphs. In this paper we present the full survey of the available results on the theory of word-representable graphs and the most recent achievements in this field.

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Authors and Affiliations

  1. University of Strathclyde, Livingstone Tower, 26 Richmond St., Glasgow, G1 1XH, UK

    S. V. Kitaev

  2. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. V. Pyatkin

  3. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    A. V. Pyatkin

Authors
  1. S. V. Kitaev
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  2. A. V. Pyatkin
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Correspondence to S. V. Kitaev.

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Original Russian Text © S.V. Kitaev, A.V. Pyatkin, 2018, published in Diskretnyi Analiz i Issledovanie Operatsii, 2018, Vol. 25, No. 2, pp. 19–53.

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Kitaev, S.V., Pyatkin, A.V. Word-Representable Graphs: a Survey. J. Appl. Ind. Math. 12, 278–296 (2018). https://doi.org/10.1134/S1990478918020084

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