Word-Representable Graphs: a Survey

Word-Representable Graphs: a Survey 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied and Industrial Mathematics Springer Journals

Word-Representable Graphs: a Survey

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Publisher
Pleiades Publishing
Copyright
Copyright © 2018 by Pleiades Publishing, Ltd.
Subject
Mathematics; Mathematics, general
ISSN
1990-4789
eISSN
1990-4797
D.O.I.
10.1134/S1990478918020084
Publisher site
See Article on Publisher Site

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 ∈ 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.

Journal

Journal of Applied and Industrial MathematicsSpringer Journals

Published: May 29, 2018

References

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