An in-depth account of graph theory, written for serious students of
mathematics and computer science. It reflects the current state of the
subject and emphasises connections with other branches of pure
mathematics. Recognising that graph theory is one of several courses
competing for the attention of a student, the book contains extensive
descriptive passages designed to convey the flavour of the subject and
to arouse interest. In addition to a modern treatment of the classical
areas of graph theory, the book presents a detailed account of newer
topics, including Szemerédis Regularity Lemma and its use, Shelahs
extension of the Hales-Jewett Theorem, the precise nature of the phase
transition in a random graph process, the connection between electrical
networks and random walks on graphs, and the Tutte polynomial and its
cousins in knot theory. Moreover, the book contains over 600 well
thought-out exercises: although some are straightforward, most are
substantial, and some will stretch even the most able reader.Download
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