Related papers: Simultaneous Embedding of a Planar Graph and Its D…

In this paper we introduce the 'simultaneous membership problem', defined for any graph class C characterized in terms of representations, e.g. any class of intersection graphs. Two graphs G_1 and G_2, sharing some vertices X (and the…

We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…

Consider two planar graphs which are subject to edge insertions and deletions. We show that whether the two graphs are isomorphic can be maintained with first-order logic formulas and auxiliary data of polynomial size. This places the…

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…

Tutte's spring embedding theorem states that, for a three-connected planar graph, if the outer face of the graph is fixed as the complement of some convex region in the plane, and all other vertices are placed at the mass center of their…

While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…

Given an undirected planar graph G with n vertices and a set S of n points inside a simple polygon P, a point-set embedding of G on S is a planar drawing of G such that each vertex is mapped to a distinct point of S and the edges are…

We address the problem of computing a dynamic visualization of a geometric graph $G$ as a sequence of frames. Each frame shows only a portion of the graph but their union covers $G$ entirely. The two main requirements of our dynamic…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

A graph with n vertices is 1-planar if it can be drawn in the plane such that each edge is crossed at most once, and is optimal if it has the maximum of 4n-8 edges. We show that optimal 1-planar graphs can be recognized in linear time. Our…

Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

We show how to test in linear time whether an outerplanar graph admits a planar rectilinear drawing, both if the graph has a prescribed plane embedding that the drawing has to respect and if it does not. Our algorithm returns a planar…

Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of…

Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…

We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…

A (possibly denerate) drawing of a graph $G$ in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph…

The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However,…

Recently, there have been some breakthroughs in graph analysis by applying the graph neural networks (GNNs) following a neighborhood aggregation scheme, which demonstrate outstanding performance in many tasks. However, we observe that the…

We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected…