Related papers: On Counting Constructions and Isomorphism Classes …

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…

Consider the geometric graph on $n$ independent uniform random points in a connected compact region $A$ of ${\bf R}^d, d \geq 2$, with $C^2$ boundary, or in the unit square, with distance parameter $r_n$. Let $K_n$ be the number of…

Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.

In this article, we study the properties of $\psi$-amicable numbers. We prove that their asymptotic density relative to the positive integers is zero. We also propose generalizations of $\psi$-amicable numbers.

We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges…

For a random intersection graph with a power law degree sequence having a finite mean and an infinite variance we show that the global clustering coefficient admits a tunable asymptotic distribution.

Asymptotic properties of random graph sequences, like occurrence of a giant component or full connectivity in Erd\H{o}s-R\'enyi graphs, are usually derived with very specific choices for defining parameters. The question arises to which…

We consider the distribution of the major index on standard tableaux of arbitrary straight shape and certain skew shapes. We use cumulants to classify all possible limit laws for any sequence of such shapes in terms of a simple auxiliary…

Let A be a minor-closed class of labelled graphs, and let G_n be a random graph sampled uniformly from the set of n-vertex graphs of A. When n is large, what is the probability that G_n is connected? How many components does it have? How…

We prove two estimates for the expectation of the exponential of a complex function of a random permutation or subset. Using this theory, we find asymptotic expressions for the expected number of copies and induced copies of a given graph…

We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…

Let $D^-$ and $D^+$ be properly immersed closed locally convex subsets of a Riemannian manifold with pinched negative sectional curvature. Using mixing properties of the geodesic flow, we give an asymptotic formula as $t\to+\infty$ for the…

We consider random subgroups of Thompson's group $F$ with respect to two natural stratifications of the set of all $k$ generator subgroups. We find that the isomorphism classes of subgroups which occur with positive density are not the same…

We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank…

A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers.

For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…

We give explicit formulas for the asymptotic Betti numbers of the unordered configuration spaces of an arbitrary finite graph over an arbitrary field.

We introduce the extension graph of graph product of groups and study its geometry. This enables us to study properties of graph product by exploiting large scale geometry of its defining graph. In particular, we show that the extension…

Answering a question of Kolaitis and Kopparty, we show that, for given integer $q>1$ and pairwise nonisomorphic connected graphs $G_1...G_k$, if $p=p(n) $ is such that $\Pr(G_{n,p}\supseteq G_i)\to 1$ $\forall i$, then, with $\xi_i$ the…

We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…