Geodesic
Word-representable graphs: a~survey
Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 2, pp. 19-53

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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 $xyxy\dots$ or a word $yxyx\dots$ (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, word, pattern.
Mots-clés : orientation 
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     author = {s. V. Kitaev and A. V. Pyatkin},
     title = {Word-representable graphs: a~survey},
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     publisher = {mathdoc},
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     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2018_25_2_a1/}
}
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s. V. Kitaev; A. V. Pyatkin. Word-representable graphs: a~survey. Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 2, pp. 19-53. http://geodesic.mathdoc.fr/item/DA_2018_25_2_a1/