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PMSP - Regularity Lemmas in graph theory, additive combinatorics and TCS I - Luca Trevisan
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The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace.
Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs.
Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject.
It is this aspect of the book which should guarantee it a permanent place in the literature. More Mathematics.
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