Ann N. Trenk Martin Charles GolumbicCambridge University Press, 2/12/2004EAN 9780521827584, ISBN10: 0521827582Hardcover, 278 pages, 23.6 x 15.8 x 1.9 cmLanguage: EnglishThe study of algorithmic graph theory and structured families of graphs is an important branch of discrete mathematics. It finds numerous applications, from data transmission through networks to efficiently scheduling aircraft and crews, as well as contributing to breakthroughs in genetic analysis and studies of the brain. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. One of these is the study of tolerance graphs and tolerance orders. This book contains the first thorough study of tolerance graphs and related topics, indeed the authors have included proofs of major results previously unpublished in book form. It will act as a springboard for researchers, and especially graduate students, to pursue new directions of investigation. With many examples and exercises it is also suitable for use as the text for a graduate course in graph theory.1. Introduction2. Early work on tolerance graphs3. Trees, cotrees and bipartite graphs4. Interval probe graphs5. Bitolerance graphs and ordered sets6. Unit and 50% tolerance graphs7. Comparability and invariance results8. Bounded bitolerance recognition9. Algorithms on tolerance graphs10. The hierarchy of bitolerance orders11. Tolerance models on trees12. Phi-tolerance models13. Directed tolerance graphs14. Open questions and further directions.' ... great value to researchers in the field, and it can also be used as a graduate text in graph theory, since many examples and exercises have been included.' Zentralblatt MATH
