Related papers: Sequence mixed graphs
This paper investigates quasi-isometries between graphs with variable edge lengths. A quasi-isometry is a mapping between metric spaces that approximately preserves distances, allowing for a bounded amount of additive and multiplicative…
The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to…
A graph G on n vertices is said to be extendable if G can be modified to form a new graph H on more than n vertices, while preserving the degrees of the vertices common to G and H. The added vertices all have the same degree and we define…
This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of $d$-compatible map for the pairs of a complete graph and an arbitrary graph, and using it, we give a combinatorial lower bound for the…
A graph $H$ is an \emph{isometric} subgraph of $G$ if $d_H(u,v)= d_G(u,v)$, for every pair~$u,v\in V(H)$. A graph is \emph{distance preserving} if it has an isometric subgraph of every possible order. A graph is \emph{sequentially distance…
This paper explores the properties of directed graphs, termed generalized action graphs, which exhibit a strong connection to certain number sequences. Focusing on the structural and combinatorial aspects, we investigate the conditions…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
The \emph{distance-number} of a graph $G$ is the minimum number of distinct edge-lengths over all straight-line drawings of $G$ in the plane. This definition generalises many well-known concepts in combinatorial geometry. We consider the…
Given a set of nonempty subsets of some universal set, their intersection graph is defined as the graph with one vertex for each set and two vertices are adjacent precisely when their representing sets have non-empty intersection. Sometimes…
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…
Many degree sequences can only be realised in graphs that contain a `ds-completable card', defined as a vertex-deleted subgraph in which the erstwhile neighbours of the deleted vertex can be identified from their degrees, if one knows the…
Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). We introduce a special kind of simple drawings that we call generalized…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
In this paper we provide a principled approach to solve a transductive classification problem involving a similar graph (edges tend to connect nodes with same labels) and a dissimilar graph (edges tend to connect nodes with opposing…
For a graph $G$ spanning a metric space, the dilation of a pair of points is the ratio of their distance in the shortest path graph metric to their distance in the metric space. Given a graph $G$ and a budget $k$, a classic problem is to…
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a 3-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily 3-connected i.e. the sequence…
A multigraph is exactly k-edge-connected if there are exactly k edge-disjoint paths between any pair of vertices. We characterize the class of exactly 3-edge-connected graphs, giving a synthesis involving two operations by which every…
We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…
Consider two horizontal lines in the plane. A pair of a point on the top line and an interval on the bottom line defines a triangle between two lines. The intersection graph of such triangles is called a simple-triangle graph. This paper…