Random Graphs, Geometry and Asymptotic Structure - Michael Krivelevich, Konstantinos Panagiotou, Mathew Penrose, Colin McDiarmid

Random Graphs, Geometry and Asymptotic Structure

Buch | Hardcover
127 Seiten
2016
Cambridge University Press (Verlag)
978-1-107-13657-1 (ISBN)
78,55 inkl. MwSt
A self-contained and concise introduction to recent developments, particularly those of a geometric and topological nature, in the theory of random graphs. Such material is seldom covered in the formative study of young combinatorialists and probabilists, making this essential reading for beginning researchers in these fields.
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.

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.

Editors' introduction; Part I. Long Paths and Hamiltonicity in Random Graphs: 1. Introduction; 2. Tools; 3. Long paths in random graphs; 4. The appearance of Hamilton cycles in random graphs; References for Part I; Part II. Random Graphs from Restricted Classes: 1. Introduction; 2. Random trees; 3. Random graphs from block-stable classes; References for Part II; Part III. Lectures on Random Geometric Graphs: 1. Introduction; 2. Edge counts; 3. Edge counts: normal approximation; 4. The maximum degree; 5. A sufficient condition for connectivity; 6. Connectivity and Hamiltonicity; 7. Solutions to exercises; References for Part III; Part IV. On Random Graphs from a Minor-closed Class: 1. Introduction; 2. Properties of graph classes; 3. Bridge-addability, being connected and the fragment; 4 Growth constants; 5. Unlabelled graphs; 6. Smoothness; 7. Concluding remarks; References for Part IV; Index.

Erscheinungsdatum
Reihe/Serie London Mathematical Society Student Texts
Zusatzinfo 1 Tables, black and white; 2 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 158 x 235 mm
Gewicht 310 g
Themenwelt Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 1-107-13657-1 / 1107136571
ISBN-13 978-1-107-13657-1 / 9781107136571
Zustand Neuware
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