Related papers: Recognizing Weighted Disk Contact Graphs
Octilinear graph drawings are a standard paradigm extending the orthogonal graph drawing style by two additional slopes (+1 and -1). We are interested in two constrained drawing problems where the input specifies a so-called representation,…
We study the recognition complexity of subgraphs of k-connected planar cubic graphs for k = 1, 2, 3. We present polynomial-time algorithms to recognize subgraphs of 1- and 2-connected planar cubic graphs, both in the variable and fixed…
The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of…
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
We investigate the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding…
An obstacle representation of a plane graph G is V(G) together with a set of opaque polygonal obstacles such that G is the visibility graph on V(G) determined by the obstacles. We investigate the problem of computing an obstacle…
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often…
A long-standing conjecture by Heath, Pemmaraju, and Trenk states that the upward book thickness of outerplanar DAGs is bounded above by a constant. In this paper, we show that the conjecture holds for subfamilies of upward outerplanar…
Given a set $P$ of $n$ points in the plane and a collection of disks centered at these points, the disk graph $G(P)$ has vertex set $P$, with an edge between two vertices if their corresponding disks intersect. We study the dominating set…
We introduce and study the problem of balanced districting, where given an undirected graph with vertices carrying two types of weights (different population, resource types, etc) the goal is to maximize the total weights covered in vertex…
In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These…
The $n$-$book ~embedding$ of a graph $G$ is an embedding of the graph $G$ in an $n$-book with the vertices of $G$ on the spine and each edge to the pages without crossing each other. If the degree of vertices of $G$ at most one in each…
A temporal graph is a graph in which edges are assigned a time label. Two nodes u and v of a temporal graph are connected one to the other if there exists a path from u to v with increasing edge time labels. We consider the problem of…
An elimination tree of a connected graph $G$ is a rooted tree on the vertices of $G$ obtained by choosing a root $v$ and recursing on the connected components of $G-v$ to obtain the subtrees of $v$. The graph associahedron of $G$ is a…
An outerplanar graph is a planar graph that has a planar drawing with all vertices on the unbounded face. The matching complex of a graph is the simplicial complex whose faces are subsets of disjoint edges of the graph. In this paper we…
In this paper we prove that the \textsc{Min-Bisection} problem is NP-hard on \emph{unit disk graphs}, thus solving a longstanding open question.
We initiate a systematic study of approximation schemes for fundamental optimization problems on disk graphs, a common generalization of both planar graphs and unit-disk graphs. Our main contribution is a general framework for designing…