Related papers: A new bound in Majority Dynamics on Random Graphs

Denote by $K_p(n,k)$ the random subgraph of the usual Kneser graph $K(n,k)$ in which edges appear independently, each with probability $p$. Answering a question of Bollob\'as, Narayanan, and Raigorodskii,we show that there is a fixed $p<1$…

For a $\Delta$-regular connected graph ${\sf H}$ the problem of determining the upper tail large deviation for the number of copies of ${\sf H}$ in $\mathbb{G}(n,p)$, an Erd\H{o}s-R\'{e}nyi graph on $n$ vertices with edge probability $p$,…

We study the relaxation dynamics of fully clustered networks (maximal number of triangles) to an unclustered state under two different edge dynamics---the double-edge swap, corresponding to degree-preserving randomization of the…

As an application of Szemeredi's regularity lemma, Erdos-Frankl-Rodl (1986) showed that the number of graphs on vertex set {1,2,...n} with a monotone class P is $2^{(1+o(1))ex(n,P)n^2/2}$ where $ex(n,P)$ is the maximum number of edges of an…

In this paper, we study "robust" dominating sets of random graphs that retain the domination property even if a small \emph{deterministic} set of edges are removed. We motivate our study by illustrating with examples from wireless networks…

We consider a class of particle systems described by differential equations (both stochastic and deterministic), in which the interaction network is determined by the realization of an Erd\H{o}s-R\'enyi graph with parameter $p_n\in (0, 1]$,…

We study preferential attachment mechanisms in random graphs that are parameterized by (i) a constant bias affecting the degree-biased distribution on the vertex set and (ii) the distribution of times at which new vertices are created by…

For any graph G = (V, E) and proportion $p\in(0,1]$, a set $S\subseteq V$ is a p-dominating set if $\frac{|N[S]|}{|V|}\geq p$. The $p$-domination number $\gamma_{p}(G)$ equals the minimum cardinality of a $p$-dominating set in G. For a…

Let P_{n,m} denote the graph taken uniformly at random from the set of all planar graphs on {1,2,..., n} with exactly m(n) edges. We use counting arguments to investigate the probability that P_{n,m} will contain given components and…

We extend a result of Lyons (2016) from fractional tiling of finite graphs to a version for infinite random graphs. The most general result is as follows. Let $\bf P$ be a unimodular probability measure on rooted networks $(G, o)$ with…

Let $G = (V,E)$ be a connected directed graph on $n$ vertices. Assign values from the set $\{1,2,\dots,n\}$ to the vertices of $G$ and update the values according to the following rule: uniformly at random choose a vertex and update its…

In this paper, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push-sum algorithms to such random scenarios. Provided that an ergodicity notion,…

In this paper we consider the problem of estimating the joint upper and lower tail large deviations of the edge eigenvalues of an Erd\H{o}s-R\'enyi random graph $\mathcal{G}_{n,p}$, in the regime of $p$ where the edge of the spectrum is no…

In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…

The Erd\H{o}s-R\'enyi random graph is the simplest model for node degree distribution, and it is one of the most widely studied. In this model, pairs of $n$ vertices are selected and connected uniformly at random with probability $p$,…

Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…

We consider the following dynamics on a connected graph $(V,E)$ with $n$ vertices. Given $p>1$ and an initial opinion profile $f_0:V \to [0,1]$, at each integer step $t \ge 1$ a uniformly random vertex $v=v_t$ is selected, and the opinion…

We consider a random graph in which vertices can have one of two possible colours. Each vertex switches its colour at a rate that is proportional to the number of vertices of the other colour to which it is connected by an edge. Each edge…

A community of $n$ individuals splits into two camps, Red and Blue. The individuals are connected by a social network, which influences their colors. Everyday, each person changes his/her color according to the majority among his/her…

We consider random graphs in which the edges are allowed to be dependent. In our model the edge dependence is quite general, we call it $p$-robust random graph. It means that every edge is present with probability at least $p$, regardless…