By Bela Bollobas

An in-depth account of graph thought, written for critical scholars of arithmetic and laptop technological know-how. It displays the present kingdom of the topic and emphasises connections with different branches of natural arithmetic. Recognising that graph thought is among the classes competing for the eye of a pupil, the booklet includes huge descriptive passages designed to show the flavor of the topic and to arouse curiosity. as well as a contemporary remedy of the classical components of graph thought, the publication offers an in depth account of more recent subject matters, together with Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the proper nature of the section transition in a random graph procedure, the relationship among electric networks and random walks on graphs, and the Tutte polynomial and its cousins in knot concept. furthermore, the publication comprises over six hundred good thought-out routines: even if a few are ordinary, such a lot are enormous, and a few will stretch even the main capable reader.