Related papers: Grid-Obstacle Representations with Connections to …
We study the existence and construction of sparse supports for hypergraphs derived from subgraphs of a graph $G$. For a hypergraph $(X,\mathcal{H})$, a support $Q$ is a graph on $X$ s.t. $Q[H]$, the graph induced on vertices in $H$ is…
The visual complexity of a graph drawing can be measured by the number of geometric objects used for the representation of its elements. In this paper, we study planar graph drawings where edges are represented by few segments. In such a…
The goal of graph inference is to design algorithms for learning properties of a hidden graph using queries to an oracle that returns information about the graph. Graph reconstruction, verification, and property testing are all types of…
A two-dimensional grid consists of vertices of the form (i,j) for 1 \leq i \leq m and 1 \leq j \leq n, for fixed m,n > 1. Two vertices are adjacent if the \ell_1 distance between their vectors is equal to 1. A landmark set is a subset of…
In the classical Node-Disjoint Paths (NDP) problem, we are given an $n$-vertex graph $G=(V,E)$, and a collection $M=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of its vertices, called source-destination, or demand pairs. The goal is to route…
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…
We study the problem of embedding a guest graph with minimum edge-congestion into a multidimensional grid with the same size as that of the guest graph. Based on a well-known notion of graph separators, we show that an embedding with a…
Computing the number of realizations of a minimally rigid graph is a notoriously difficult problem. Towards this goal, for graphs that are minimally rigid in the plane, we take advantage of a recently published algorithm, which is the…
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…
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…
Graph convolutional networks (GCNs) are widely used in graph-based applications such as graph classification and segmentation. However, current GCNs have limitations on implementation such as network architectures due to their irregular…
In the Graph Reconstruction (GR) problem, the goal is to recover a hidden graph by utilizing some oracle that provides limited access to the structure of the graph. The interest is in characterizing how strong different oracles are when the…
The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices…
The directed graph reachability problem takes as input an $n$-vertex directed graph $G=(V,E)$, and two distinguished vertices $s$ and $t$. The problem is to determine whether there exists a path from $s$ to $t$ in $G$. This is a canonical…
Golumbic, Lipshteyn, and Stern defined in 2009 the class of EPG graphs, the intersection graph class of edge paths on a grid. An EPG graph $G$ is a graph that admits a representation where its vertices correspond to paths in a grid $Q$,…
We exactly settle the complexity of graph realization, graph rigidity, and graph global rigidity as applied to three types of graphs: "globally noncrossing" graphs, which avoid crossings in all of their configurations; matchstick graphs,…
Let $P$ be a set of $n \geq 5$ points in convex position in the plane. The path graph $G(P)$ of $P$ is an abstract graph whose vertices are non-crossing spanning paths of $P$, such that two paths are adjacent if one can be obtained from the…
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…
In this paper, we are interested in the edge intersection graphs of paths of a grid where each path has at most one bend, called B1-EPG graphs and first introduced by Golumbic et al (2009). We also consider a proper subclass of B1-EPG, the…
In this paper we study threshold coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is…