TY - JOUR

T1 - Word-Representable Graphs

T2 - a Survey

AU - Kitaev, S. V.

AU - Pyatkin, A. V.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - 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 ∈ 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.

AB - 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 ∈ 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.

KW - orientation

KW - pattern

KW - representation of graphs

KW - word

UR - http://www.scopus.com/inward/record.url?scp=85047875062&partnerID=8YFLogxK

U2 - 10.1134/S1990478918020084

DO - 10.1134/S1990478918020084

M3 - Article

AN - SCOPUS:85047875062

VL - 12

SP - 278

EP - 296

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -