New results on word-representable graphs

Andrew Collins, Sergey Kitaev, Vadim V. Lozin

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
88 Downloads (Pure)


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).
Original languageEnglish
Pages (from-to)136-141
Number of pages6
JournalDiscrete Applied Mathematics
Issue numberPart 1
Early online date20 Nov 2014
Publication statusPublished - 10 Jan 2017


  • semi-transitive orientation
  • speed of hereditary properties
  • hereditary property of graphs


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