相关论文: Independent sets in certain classes of (almost) re…

When $I$ is the edge ideal of a graph $G$, we use combinatorial properities, particularly Property $P$ on connectivity of neighbors of an edge, to classify when a binomial sum of vertices is a regular element on $R/I(G)$. Under a mild…

In this note we analyze two algorithms, one for producing a matching and one for an independent set, on $k$-uniform $d$-regular hypergraphs of large girth. As a result we obtain new lower bounds on the size of a maximum matching or…

Assessing generative models is not an easy task. Generative models should synthesize graphs which are not replicates of real networks but show topological features similar to real graphs. We introduce an approach for assessing graph…

An independent set in a graph G is a set of vertices no two of which are joined by an edge. A vertex-weighted graph associates a weight with every vertex in the graph. A vertex-weighted graph G is called a unique independence…

There are several graphs defined on groups. Among them we consider graphs whose vertex set consists conjugacy classes of a group $G$ and adjacency is defined by properties of the elements of conjugacy classes. In particular, we consider…

Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…

The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

A set of graphs is said to be independent if there is no homomorphism between distinct graphs from the set. We consider the existence problems related to the independent sets of countable graphs. While the maximal size of an independent set…

Counting dominating sets in a graph $G$ is closely related to the neighborhood complex of $G$. We exploit this relation to prove that the number of dominating sets $d(G)$ of a graph is determined by the number of complete bipartite…

We study recursively defined functions associated with directed graphs on the k dimensional nonnegative integral lattice. The existence of certain combinatorial structures associated with these function classes are shown to be independent…

We study set systems formed by neighborhoods in graphs of bounded twin-width. We start by proving that such graphs have linear neighborhood complexity, in analogy to previous results concerning graphs from classes with bounded expansion and…

We introduce methods to count and enumerate all maximal independent, all maximum independent sets, and all independent sets in threshold graphs and k-threshold graphs. Within threshold graphs and k-threshold graphs independent sets…

The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…

A self-contained exposition is given of the topological and Galois-theoretic properties of the category of combinatorial 1-complexes, or graphs, very much in the spirit of Stallings. A number of classical, as well as some new results about…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

The goal of this paper is to obtain quantitative results on the number and on the size of maximal independent sets and maximal matchings in several block-stable graph classes that satisfy a proper sub-criticality condition. In particular we…

We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…

We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…