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.
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Verlagsort
Produkt-Hinweis
Illustrationen
Worked examples or Exercises
Gewicht
ISBN-13
978-1-009-34437-1 (9781009344371)
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Schweitzer Klassifikation
Bela Bollobas has been a Fellow at Trinity College, Cambridge, for over fifty years, for decades as a Director of Studies in Mathematics, and is the Chair of Excellence in Combinatorics at the University of Memphis. He has had over seventy Ph.D. students. He is a Fellow of the Royal Society and a Foreign Member of the Hungarian Academy of Sciences and of the Polish Academy of Sciences. Among the awards he has received are a Senior Whitehead Prize, a Bocskai Prize, a Szechenyi Prize and an Honorary Doctorate from Adam Mickiewicz University, Poznan. This is his fourteenth book. Robert Morris has taught graph theory and combinatorics at IMPA, Rio de Janeiro for the past fifteen years, and has had more than twenty Ph.D. and Masters students. He is a Member of the Brazilian Academy of Sciences, and has been awarded numerous prizes, including the European Prize in Combinatorics, the Fulkerson Prize, the MCA Prize, and the Leroy P. Steele Prize for Seminal Contribution to Research. His first book was awarded the Elon Lages Lima Prize by the Brazilian Mathematical Society. This is his second book.
Autor*in
University of Cambridge
IMPA, Rio de Janeiro
Introduction; 1. Basic graph theory; 2. Extremal graph theory; 3. Classical graph theory; 4. Ramsey theory; 5. Random graphs.
