Related papers: On Touching Triangle Graphs
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on…
Weak unit disk contact graphs are graphs that admit representing nodes as a collection of internally disjoint unit disks whose boundaries touch if there is an edge between the corresponding nodes. In this work we focus on graphs without…
A word-representable graph is a simple graph $G$ which can be represented by a word $w$ over the vertices of $G$ such that any two vertices are adjacent in $G$ if and only if they alternate in $w$. It is known that the class of…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can…
We consider embeddings of 3-regular graphs into 3-dimensional Cartesian coordinates, in such a way that two vertices are adjacent if and only if two of their three coordinates are equal (that is, if they lie on an axis-parallel line) and…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
We show that the problem of identifying different signal components from a time-frequency representation can be equivalently phrased as a graph clustering problem: given a graph $G=(V,E)$ one aims to identify `clusters', subgraphs that are…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex $u$ is represented by a geometric object $R(u)$ and in which each edge $(u,v)$ is represented…
We show that every graph of maximum degree 3 can be represented as the intersection graph of axis parallel boxes in three dimensions, that is, every vertex can be mapped to an axis parallel box such that two boxes intersect if and only if…
Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
We show how to test the bipartiteness of an intersection graph of n line segments or simple polygons in the plane, or of balls in R^d, in time O(n log n). More generally we find subquadratic algorithms for connectivity and bipartiteness…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of…