Basic Graph Theory - Béla Bollobás

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Résumé :
Over the past few decades, graph theory has developed into one of the central areas of modern mathematics, with close (and growing) connections to areas of pure mathematics such as number theory, probability theory, algebra and geometry, as well as to applied areas such as the theory of networks, machine learning, statistical physics, and biology. It is a young and vibrant area, with several major breakthroughs having occurred in just the past few years. This book offers the reader a gentle introduction to the fundamental concepts and techniques of graph theory, covering classical topics such as matchings, colourings and connectivity, alongside the modern and vibrant areas of extremal graph theory, Ramsey theory, and random graphs. The focus throughout is on beautiful questions, ideas and proofs, and on illustrating simple but powerful techniques, such as the probabilistic method, that should be part of every young mathematician's toolkit....

Biographie:
B?la Bollob?s has been a fellow at Trinity College, Cambridge, for over 55 years, for decades as Director of Studies in Mathematics, and is the Chair of Excellence in Combinatorics at the University of Memphis. He has supervised over 70 PhD students. He is a fellow of the Royal Society, a foreign member of the Hungarian, Polish and Brazilian Academies of Sciences. Among the awards he has received are the Senior Whitehead Prize, the Sz?chenyi Prize, an Honorary Doctorate from Adam Mickiewicz University, Pozn?, and the Commander's Cross of the Hungarian Order of Merit. This is his 14th book....

Sommaire:
Introduction...