The component sizes of a critical random graph

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Table of contents

1 Introduction 
1.1 Chaînes de fragmentation
1.2 Résultats généraux sur les fragmentations
1.3 Les arbres de fragmentation
1.4 Le quadtree
1.5 Graphes aléatoires
1.6 Les tailles des composantes d’un graphe aléatoire critique
2 A phase transition for the heights of a fragmentation tree 
2.1 Introduction
2.2 Formulation of the main results
2.3 Preliminaries
2.4 Study of the heights
2.5 Study of the saturation levels
2.6 An explanation for the phase transition
3 Partial match queries in two-dimensional quadtrees 
3.1 Introduction
3.2 Notation and first properties
3.3 Particular cases and fragmentation theory
3.4 The convergence at fixed x ∈ (0, 1)
3.5 Identifying the limit
3.6 Extensions and comments
4 The component sizes of a critical random graph 
4.1 Introduction
4.2 Formulation of the results
4.3 The depth-first search
4.4 Convergence of the walk sn
4.5 Study of the cycle half-edges
4.6 Study of the random simple graph SGn
4.7 The power law distribution setting
Bibliographie