Related papers: Threshold graph limits and random threshold graphs

We generalize the concept of token graphs to obtain supertoken graphs. In the latter case, there can be more than one token in a vertex. We formally define supertoken graphs and establish their basic properties. Moreover, we provide some…

The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.

We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…

The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in…

Let G = (V, E) be a finite simple connected graph. We say a graph G realizes a code of the type 0^s_1 1^t_1 0^s_2 1^t_2 ... 0^s_k1^t_k if and only if G can obtained from the code by some rule. Some classes of graphs such as threshold and…

This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.

In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…

Bounds on the minimum degree and on the number of vertices at- taining it have been much studied for finite edge-/vertex-minimally k- connected/k-edge-connected graphs. We give an overview of the results known for finite graphs, and show…

Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in…

In the paper we give a lower bound for the number of vertices of a given graph using its chromatic number. We find the graphs for which this bound is exact. The results are applied in the theory of Foklman numbers.

We apply in this article (non rigorous) statistical mechanics methods to the problem of counting long circuits in graphs. The outcomes of this approach have two complementary flavours. On the algorithmic side, we propose an approximate…

We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…

Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…

We introduce a method for the theoretical analysis of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and…

In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…

We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to…

We survey recent advances in the theory of graph and hypergraph decompositions, with a focus on extremal results involving minimum degree conditions. We also collect a number of intriguing open problems, and formulate new ones.

A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. We establish tight lower bounds on the maximum size of a uniquely restricted matching in terms of order, size, and maximum degree.

A limit theorem for a sequence of diffusion processes on graphs is proved in a case when vary both parameters of the processes (the drift and diffusion coefficients on every edge and the asymmetry coefficients in every vertex), and…