Review of Words and Graphs by Sergey Kitaev and Vadim Lozin

Abstract

Two distinct letters x and y in a word alternate if, after deleting all other letters in the word, the resulting word is of the form xyxy : : : or yxyx : : : . A graph G = (V;E) is word-representable if there exists a word w over the alphabet V such that the letters x and y alternate in w if and only if there is an edge connecting x and y in G. If graphs can be represented by words then exciting new possibilities arise for investigating graph properties in terms of the properties of the words that represent them. In addition, words (i.e. strings) would offer an additional way of storing and manipulating graph structures in computation. This textbook is a comprehensive survey of word-representable graphs and the relationships between combinatorics on words and graph properties. The contents are accessible to graph theorists, formal language theorists, computer scientists, and students who have some familiarity with graph theory and words.