The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.

About the Authors

Professor Michael Krivelevich is a renowned expert on the theory of random graphs. He has written over 170 research papers, more than 100 of them in the last ten years. Most of his publications are on random graphs and related fields, such as extremal combinatorics, positional games theory and theoretical computer science.

Professor Konstantinos Panagiotou received the Richard Rado Prize in 2010. He is an expert on the relatively new theory of Boltzmann samplers and its relations to the study of random planar graphs as well as random graphs with constraints.

Professor Mathew Penrose is a leading expert on the theory of random geometric graphs. His research interests cover a variety of topics in modern probability theory, often motivated by questions from the physical sciences. These include interacting particle systems, percolation, stochastic analysis and extreme value theory.

Professor Colin McDiarmid is a leading expert on probabilistic combinatorics and discrete probability theory, with several participations in editorial boards of leading combinatorics journals. He has published over 80 papers on these areas. He is one of the pioneers of the theory of random planar graphs and random graphs with constraints.

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