Displaying similar documents to “Isolated trees in a bichromatic random graph”

Random Walks and Trees

Zhan Shi (2011)

ESAIM: Proceedings

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These notes provide an elementary and self-contained introduction to branching random walks. Section 1 gives a brief overview of Galton–Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-goût to the main part, Section 3, where branching...

Asymptotic properties of random graphs

Zbigniew Palka

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CONTENTS1. Introduction...........................................................................5  1.1. Purpose and scope..........................................................5  1.2. Probability-theoretic preliminaries....................................6  1.3. Graphs............................................................................11  1.4. Random graphs..............................................................132. Vertex-degrees....................................................................15  2.1....

The sizes of components in random circle graphs

Ramin Imany-Nabiyyi (2008)

Discussiones Mathematicae Graph Theory

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We study random circle graphs which are generated by throwing n points (vertices) on the circle of unit circumference at random and joining them by an edge if the length of shorter arc between them is less than or equal to a given parameter d. We derive here some exact and asymptotic results on sizes (the numbers of vertices) of "typical" connected components for different ways of sampling them. By studying the joint distribution of the sizes of two components, we "go into" the structure...