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Displaying similar documents to “Infinite paths and cliques in random graphs”

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...

A note on domination parameters in random graphs

Anthony Bonato, Changping Wang (2008)

Discussiones Mathematicae Graph Theory

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Domination parameters in random graphs G(n,p), where p is a fixed real number in (0,1), are investigated. We show that with probability tending to 1 as n → ∞, the total and independent domination numbers concentrate on the domination number of G(n,p).

The Chromatic Number of Random Intersection Graphs

Katarzyna Rybarczyk (2017)

Discussiones Mathematicae Graph Theory

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We study problems related to the chromatic number of a random intersection graph G (n,m, p). We introduce two new algorithms which colour G (n,m, p) with almost optimum number of colours with probability tending to 1 as n → ∞. Moreover we find a range of parameters for which the chromatic number of G (n,m, p) asymptotically equals its clique number.

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....