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Diskretn. Anal. Issled. Oper., 2018, Volume 25, Issue 2, Pages 19–53 (Mi da894)  

Word-representable graphs: a survey

s. V. Kitaeva, A. V. Pyatkinbc

a University of Strathclyde, Livingstone Tower, 26 Richmond St., Glasgow, G1 1XH, UK
b Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
c Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

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 $xy\in E$. 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. Tab. 2, illustr. 11, bibliogr. 48.

Keywords: representation of graphs, orientation, word, pattern.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.5.1, 0314-2016-0014


DOI: https://doi.org/10.17377/daio.2018.25.588

Full text: PDF file (1075 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:2, 278–296

UDC: 519.174
Received: 11.08.2017
Revised: 12.12.2018

Citation: s. V. Kitaev, A. V. Pyatkin, “Word-representable graphs: a survey”, Diskretn. Anal. Issled. Oper., 25:2 (2018), 19–53; J. Appl. Industr. Math., 12:2 (2018), 278–296

Citation in format AMSBIB
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\by s.~V.~Kitaev, A.~V.~Pyatkin
\paper Word-representable graphs: a~survey
\jour Diskretn. Anal. Issled. Oper.
\yr 2018
\vol 25
\issue 2
\pages 19--53
\mathnet{http://mi.mathnet.ru/da894}
\crossref{https://doi.org/10.17377/daio.2018.25.588}
\elib{https://elibrary.ru/item.asp?id=34875789}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 2
\pages 278--296
\crossref{https://doi.org/10.1134/S1990478918020084}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047875062}


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