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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 readers 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.
beia bOllObas 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 Szechenyi Prize, an Honorary Doctorate from Adam Mickiewicz University, Poznan, and the Commander’s Cross of the Hungarian Order of Merit. This is his 14th book.
robert morris has taught graph theory and combinatorics at IMPA, Rio de Janeiro, for the past 15 years and has had more than 20 PhD and Master’s 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.