This is the first book to offer a complete account of the theory of simplicial decompositions of graphs, possibly the single most important tool in infinite graph theory. The text is centered on a number of guiding problems and concepts such as the existence and uniqueness problem of simplicial decompositions into primes, and the concept of excluded minors as a means of identifying a desired structure. Following theoretical developments since the 1930s, the author includes extensive information on the current state of research, as well as many examples, proof strategies, exercises, and...

Almosttwodecadeshavepassedsincetheappearanceofthosegrapht- ory texts that still set the agenda for most introductory courses taught today. The canon created by those books has helped to identify some main?eldsofstudyandresearch, andwilldoubtlesscontinuetoin?uence the development of the discipline for some time to come. Yet much has happened in those 20 years, in graph theory no less thanelsewhere: deepnewtheoremshavebeenfound, seeminglydisparate methods and results have become interrelated, entire new branches have arisen. To name just a few such developments, one may think of how the new...

The fourth edition of this standard textbook of modern graph theory has been revised, updated, and substantially extended. Covering all major recent developments, it can be used both as a reliable textbook for an introductory course and as a graduate text.