Related papers: Simultaneous Embedding of a Planar Graph and Its D…
We describe a construction for embeddings of complete graphs where the dual has a cutvertex and the genus is close to the minimum genus of the primal graph. When the number of vertices is congruent to 5 modulo 12, we further guarantee that…
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency…
Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…
There are many representations of planar graphs, but few are as elegant as Tur\'an's (1984): it is simple and practical, uses only 4 bits per edge, can handle self-loops and multi-edges, and can store any specified embedding. Its main…
An embedding of a graph in a book, called book embedding, consists of a linear ordering of its vertices along the spine of the book and an assignment of its edges to the pages of the book, so that no two edges on the same page cross. The…
In this paper we describe a physical problem, based on electromagnetic fields, whose topological constraints are higher dimensional versions of Kirchhoff's laws, involving $2-$ simplicial complexes embedded in $\mathbb{R} ^3$ rather than…
Point-set embeddings and large-angle crossings are two areas of graph drawing that independently have received a lot of attention in the past few years. In this paper, we consider problems in the intersection of these two areas. Given the…
Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges…
We consider the problem of deciding whether an input graph G admits a topological embedding into a two-dimensional simplicial complex C. This problem includes, among others, the embeddability problem of a graph on a surface and the…
We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a…
We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic…
In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface S of genus g and produce a planar drawing of G in R^2, with a bounding face defined by a polygonal…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
We give a parallel $O(\log(n))$-time algorithm on a CRCW PRAM to assign vertical and horizontal segments to the vertices of any planar bipartite graph $G$ in the following manner: i) Two segments cannot share an interior point ii) Two…
We present the first algorithm to morph graphs on the torus. Given two isotopic essentially 3-connected embeddings of the same graph on the Euclidean flat torus, where the edges in both drawings are geodesics, our algorithm computes a…
A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…
In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space…
We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding $\varphi:G\rightarrow M$ of a graph $G$ into a 2-manifold $M$ maps the vertices in $V(G)$ to distinct points and the…
In an upward planar 2-slope drawing of a digraph, edges are drawn as straight-line segments in the upward direction without crossings using only two different slopes. We investigate whether a given upward planar digraph admits such a…
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large…