New results on word-representable graphs

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Collins, Andrew and Kitaev, Sergey and Lozin, Vadim V. (2017) New results on word-representable graphs. Discrete Applied Mathematics, 216 (Part 1). pp. 136-141. ISSN 0166-218X (https://doi.org/10.1016/j.dam.2014.10.024)

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Abstract

A graph G=(V,E)G=(V,E) is word-representable if there exists a word ww over the alphabet VV such that letters xx and yy alternate in ww if and only if (x,y)∈E(x,y)∈E for each x≠yx≠y. The set of word-representable graphs generalizes several important and well-studied graph families, such as circle graphs, comparability graphs, 3-colorable graphs, graphs of vertex degree at most 3, etc. By answering an open question from Halldórsson et al. (2011), in the present paper we show that not all graphs of vertex degree at most 4 are word-representable. Combining this result with some previously known facts, we derive that the number of nn-vertex word-representable graphs is View the MathML source2n23+o(n2).

ORCID iDs

Collins, Andrew, Kitaev, Sergey ORCID logoORCID: https://orcid.org/0000-0003-3324-1647 and Lozin, Vadim V.;
  • Item type:Article
    ID code:50503
    Dates:
    Date
    Event
    10 January 2017
    Published
    20 November 2014
    Published Online
    28 October 2014
    Accepted
    Notes:“NOTICE: this is the author’s version of a work that was accepted for publication in Discrete Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Applied Mathematics, [VOL 216, Part 1, (20/11/14)] DOI: 10.1016/j.dam.2014.10.024¨
    Subjects:Science > Mathematics
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:24 Nov 2014 16:29
    Last modified:11 Nov 2024 10:52
    URI:https://strathprints.strath.ac.uk/id/eprint/50503
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