Words and Graphs - Kitaev, Sergey; Lozin, Vadim; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2015)
This is the first comprehensive introduction to the theory of word-representable graphs, a generalization of several classical classes of graphs, and a new topic in discrete mathematics. After extensive introductory chapters that explain the context and consolidate the state of the art in this field, including a chapter on hereditary classes of graphs, the authors suggest a variety of problems and directions for further research, and they discuss interrelations of words and graphs in the literature by means other than word-representability. The book is self-contained, and is suitable for both reference and learning, with many chapters containing exercises and solutions to seleced problems. It will be valuable for researchers and graduate and advanced undergraduate students in discrete mathematics and theoretical computer science, in particular those engaged with graph theory and combinatorics, and also for specialists in algebra. .
Introduction -- Hereditary Classes of Graphs -- What Word-Representable Graphs Are and Where They Come From -- Characterization of Word-Representable Graphs in Terms of Semi-transitive Orientations -- Various Results on Word-Representable Graphs -- Open Problems and Further Research Directions on Word-Representable Graphs -- Interrelations Between Words and Graphs in the Literature -- More on Interrelations Between Words and Graphs in the Literature -- App. A: Graph Theory Background -- App. B: Beyond Graph Theory Background.
Keywords: Information theory; Computer science; Algebra; Theory of Computation; Mathematics of Computing; Algebra