A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
Inhaltsangabe
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.
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.
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