A Comprehensive Introduction to the Theory of Word-Representable Graphs

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 xy is an element of E. 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.