Related papers: Opinion Forming in Erdos-Renyi Random Graph and Ex…

For graphs $G_0$, $G_1$ and $G_2$, write $G_0\longmapsto(G_1, G_2)$ if each red-blue-edge-coloring of $G_0$ yields a red $G_1$ or a blue $G_2$. The Ramsey number $r(G_1, G_2)$ is the minimum number $n$ such that the complete graph…

In this paper, we study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed…

The paper is devoted to the spreading of a message within the random graph evolving by the Norros-Reittu preferential attachment model. The latter model forms random Poissonian numbers of edges between newly added nodes and existing ones.…

There are a number of well-known problems and conjectures about partitioning graphs to satisfy local constraints. For example, the majority colouring conjecture of Kreutzer, Oum, Seymour, van der Zypen and Wood states that every directed…

We show that Erd\H{o}s-R\'enyi random graphs $G(n,p)$ with constant density $p<1$ have correspondence chromatic number $O(n/\sqrt{\log n})$; this matches a prediction from linear Hadwiger's conjecture for correspondence coloring. The proof…

Consider the following random process: The vertices of a binomial random graph $G_{n,p}$ are revealed one by one, and at each step only the edges induced by the already revealed vertices are visible. Our goal is to assign to each vertex one…

We prove that with high probability over the choice of a random graph $G$ from the Erd\H{o}s-R\'enyi distribution $G(n,1/2)$, a natural $n^{O(\varepsilon^2 \log n)}$-time, degree $O(\varepsilon^2 \log n)$ sum-of-squares semidefinite program…

We consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph with average connectivity $<k>$ scaling as a power law with the number of neurons in…

Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two…

We consider vertex partitions of the binomial random graph $G_{n,p}$. For $np\to\infty$, we observe the following phenomenon: in any partition into asymptotically fewer than $\chi(G_{n,p})$ parts, i.e. $o(np/\log np)$ parts, one part must…

Approximate random k-colouring of a graph G=(V,E) is a very well studied problem in computer science and statistical physics. It amounts to constructing a k-colouring of G which is distributed close to Gibbs distribution, i.e. the uniform…

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 $p$,…

A path in an edge-colored graph is called a proper path if no two adjacent edges of the path are colored the same. For a connected graph $G$, the proper connection number $pc(G)$ of $G$ is defined as the minimum number of colors needed to…

Let $G=(V,E)$ be a $d$-regular graph on $n$ vertices and let $\mu_0$ be a probability measure on $V$. The act of moving to a randomly chosen neighbor leads to a sequence of probability measures supported on $V$ given by $\mu_{k+1} = A…

We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…

We consider the Erdos-Renyi random graph G(n,p) inside the critical window, where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous paper (arXiv:0903.4730) that considering the connected components of G(n,p) as a…

We study the graph alignment problem over two independent Erd\H{o}s-R\'enyi graphs on $n$ vertices, with edge density $p$ falling into two regimes separated by the critical window around $p_c=\sqrt{\log n/n}$. Our result reveals an…

We present a new angle on the expressive power of graph neural networks (GNNs) by studying how the predictions of real-valued GNN classifiers, such as those classifying graphs probabilistically, evolve as we apply them on larger graphs…

We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…

We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its…