New results on word-representable graphs

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).

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• Item metadata

  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:	08 Apr 2024 21:50
  URI:	https://strathprints.strath.ac.uk/id/eprint/50503