Related papers: Compact graphings
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
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.
Mixed graphs have both directed and undirected edges. A mixed cage is a regular mixed graph of given girth with minimum possible order. In this paper mixed cages are studied. Upper bounds are obtained by general construction methods and…
Proximity catch digraphs (PCDs) are based on proximity maps which yield proximity regions and are special types of proximity graphs. PCDs are based on the relative allocation of points from two or more classes in a region of interest and…
A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we explore various aspects of closed graphs, including the number of closed labelings…
In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space…
Assume that $G$ is a finite group. For every $a, b \in\mathbb N,$ we define a graph $\Gamma_{a,b}(G)$ whose vertices correspond to the elements of $G^a\cup G^b$ and in which two tuples $(x_1,\dots,x_a)$ and $(y_1,\dots,y_b)$ are adjacent if…
Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…
A lamination of a graph embedded on a surface is a collection of pairwise disjoint non-contractible simple closed curves drawn on the graph. In the case when the surface is a sphere with three punctures (a.k.a. a pair of pants), we first…
Subgraph reconfiguration is a family of problems focusing on the reachability of the solution space in which feasible solutions are subgraphs, represented either as sets of vertices or sets of edges, satisfying a prescribed graph structure…
We define a notion of (one-sided) edge shift spaces associated to ultragraphs. In the finite case our notion coincides with the edge shift space of a graph. In general, we show that our space is metrizable and has a countable basis of…
We introduce the family of $k$-gap-planar graphs for $k \geq 0$, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most $k$ of its crossings. This definition is…
Given a dense countable set in a metric space, the infinite random geometric graph is the random graph with the given vertex set and where any two points at distance less than 1 are connected, independently, with some fixed probability. It…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
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.
Many real-world datasets can be naturally represented as graphs, spanning a wide range of domains. However, the increasing complexity and size of graph datasets present significant challenges for analysis and computation. In response, graph…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
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…