Displaying similar documents to “A note on domination parameters in random graphs”

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...

Infinite paths and cliques in random graphs

Alessandro Berarducci, Pietro Majer, Matteo Novaga (2012)

Fundamenta Mathematicae

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We study the thresholds for the emergence of various properties in random subgraphs of (ℕ, <). In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.

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.

Random procedures for dominating sets in bipartite graphs

Sarah Artmann, Jochen Harant (2010)

Discussiones Mathematicae Graph Theory

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Using multilinear functions and random procedures, new upper bounds on the domination number of a bipartite graph in terms of the cardinalities and the minimum degrees of the two colour classes are established.

Poisson convergence of numbers of vertices of a given degree in random graphs

Wojciech Kordecki (1996)

Discussiones Mathematicae Graph Theory

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The asymptotic distributions of the number of vertices of a given degree in random graphs, where the probabilities of edges may not be the same, are given. Using the method of Poisson convergence, distributions in a general and particular cases (complete, almost regular and bipartite graphs) are obtained.

Generalized domination, independence and irredudance in graphs

Mieczysław Borowiecki, Danuta Michalak, Elżbieta Sidorowicz (1997)

Discussiones Mathematicae Graph Theory

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The purpose of this paper is to present some basic properties of 𝓟-dominating, 𝓟-independent, and 𝓟-irredundant sets in graphs which generalize well-known properties of dominating, independent and irredundant sets, respectively.

Expansion in finite simple groups of Lie type

Emmanuel Breuillard, Ben J. Green, Robert Guralnick, Terence Tao (2015)

Journal of the European Mathematical Society

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We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper [BGGT].

Relating 2-Rainbow Domination To Roman Domination

José D. Alvarado, Simone Dantas, Dieter Rautenbach (2017)

Discussiones Mathematicae Graph Theory

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For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination in graphs, Discrete Appl. Math. 161 (2013) 806-812] present some kind of characterization of the graphs G for which R(G) − yr2(G) = k for some integer k. Unfortunately, their result does not lead to an algorithm that allows to recognize...

Harmonic analysis of symmetric random graphs

Steffen Lauritzen (2020)

Kybernetika

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This note attempts to understand graph limits as defined by Lovasz and Szegedy in terms of harmonic analysis on semigroups. This is done by representing probability distributions of random exchangeable graphs as mixtures of characters on the semigroup of unlabeled graphs with node-disjoint union, thereby providing an alternative derivation of de Finetti's theorem for random exchangeable graphs.

Random orderings and unique ergodicity of automorphism groups

Omer Angel, Alexander S. Kechris, Russell Lyons (2014)

Journal of the European Mathematical Society

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We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group...

Domination, independence and irredundance in graphs

Jerzy Topp

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CONTENTS1. Introduction........................................................................................................ 5 1.1. Purpose and scope................................................................................. 5 1.2. Basic graphtheoretical terms................................................................ 62. Domination, independence and irredundance in graphs................................ 9 2.1. Introduction and preliminaries.................................................................

On the Complexity of Reinforcement in Graphs

Nader Jafari Rad (2016)

Discussiones Mathematicae Graph Theory

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We show that the decision problem for p-reinforcement, p-total rein- forcement, total restrained reinforcement, and k-rainbow reinforcement are NP-hard for bipartite graphs.