Related papers: Thinness of product graphs
Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the…
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of…
We investigate string graphs through the lens of graph product structure theory, which describes complicated graphs as subgraphs of strong products of simpler building blocks. A graph $G$ is called a string graph if its vertices can be…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
The independence numbers of powers of graphs have been long studied, under several definitions of graph products, and in particular, under the strong graph product. We show that the series of independence numbers in strong powers of a fixed…
We prove an inequality involving the degeneracy, the cutwidth and the sparsity of graphs. It implies a quadratic lower bound on the cutwidth in terms of the degeneracy for all graphs and an improvement of it for clique-free graphs.
Where graphs are used for modelling and specifying systems, consistency is an important concern. To be a valid model of a system, the graph structure must satisfy a number of constraints. To date, consistency has primarily been viewed as a…
Graphs on integer points of polytopes whose edges come from a set of allowed differences are studied. It is shown that any simple graph can be embedded in that way. The minimal dimension of such a representation is the fiber dimension of…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
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.
A proper edge-coloring of a graph is an interval coloring if the labels on the edges incident to any vertex form an interval of consecutive integers. Interval thickness s(G) of a graph G is the smallest number of interval colorable graphs…
We investigate Cayley graphs of graph products by showing that graph products with vertex groups that have isomorphic Cayley graphs yield isomorphic Cayley graphs.
Closeness is an important measure of network centrality. In this article we will calculate the closeness of graphs, created by using operations on graphs. We will prove a formula for the closeness of shadow graphs. We will calculate the…
This article examines the application of a popular measure of sparsity, Gini Index, on network graphs. A wide variety of network graphs happen to be sparse. But the index with which sparsity is commonly measured in network graphs is edge…
Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…
The geometric thickness of a graph G is the minimum integer k such that there is a straight line drawing of G with its edge set partitioned into k plane subgraphs. Eppstein [Separating thickness from geometric thickness. In: Towards a…
P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not…
Map vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least a unit distance apart. The plane-width of a graph is the minimum diameter of the image of the vertex set over all…