Random Graphs, Geometry and Asymptotic Structure

ISBN-13: 9781316501917 / Angielski / Miękka / 2016 / 127 str.

Michael Krivelevich; Konstantinos Panagiotou; Mathew Penrose

Opis

A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.

Recenzje

'The chapter on geometric graphs has plenty of exercises … the book will help many novices make their first steps in the field of random graphs.' Miklós Bóna, MAA Reviews (www.maa.org)

Spis treści

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.