A comprehensive introduction to the theory of word-representable graphs

Abstract

Letters x and y alternate in a word w if after deleting in w all letters but the copies of x and y we either obtain a word xyxy … (of even or odd length) or a word yxyx … (of even or odd length). A graph G = (V,E) is word-representable if and only if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if (Formula presented). Word-representable graphs generalize several important classes of graphs such as circle graphs, 3-colorable graphs and comparability graphs. This paper offers a comprehensive introduction to the theory of word-represent-able graphs including the most recent developments in the area.