Related papers: Convexity-Increasing Morphs of Planar Graphs
In a Lombardi drawing of a graph the vertices are drawn as points and the edges are drawn as circular arcs connecting their respective endpoints. Additionally, all vertices have perfect angular resolution, i.e., all angles incident to a…
Let G be a graph that may be drawn in the plane in such a way that all internal faces are centrally symmetric convex polygons. We show how to find a drawing of this type that maximizes the angular resolution of the drawing, the minimum…
Graph matching or quadratic assignment, is the problem of labeling the vertices of two graphs so that they are as similar as possible. A common method for approximately solving the NP-hard graph matching problem is relaxing it to a convex…
We consider the following two algorithmic problems: given a graph $G$ and a subgraph $H\subseteq G$, decide whether $H$ is an isometric or a geodesically convex subgraph of $G$. It is relatively easy to see that the problems can be solved…
Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically…
We investigate the problem of strong connectivity augmentation within plane oriented graphs. We show that deciding whether a plane oriented graph $D$ can be augmented with (any number of) arcs $X$ such that $D+X$ is strongly connected, but…
By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…
There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the given graph class is preserved. A graph is optimal 1-planar if…
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…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
Given a finite set $ S $ of points, we consider the following reconfiguration graph. The vertices are the plane spanning paths of $ S $ and there is an edge between two vertices if the two corresponding paths differ by two edges (one…
A multiobjective optimization problem is simplicial if the Pareto set and front are homeomorphic to a simplex and, under the homeomorphisms, each face of the simplex corresponds to the Pareto set and front of a subproblem. In this paper, we…
This paper initiates the studies of parallel algorithms for core maintenance in dynamic graphs. The core number is a fundamental index reflecting the cohesiveness of a graph, which are widely used in large-scale graph analytics. The core…
We study biplane graphs drawn on a finite planar point set $S$ in general position. This is the family of geometric graphs whose vertex set is $S$ and can be decomposed into two plane graphs. We show that two maximal biplane graphs---in the…
A well known Euler's formula consequence's corollary in graph theory states that: For a connected simple planar graph with $n$ vertices and $m$ edges, and girth $g$, we have $m \leq \frac{g}{g-2}(n-2)$. We show that a connected simple plane…
A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers specific queries pertinent to the problem at hand. In this work, we address the fully dynamic edge orientation problem, also…
We settle a problem of Dujmovi\'c, Eppstein, Suderman, and Wood by showing that there exists a function $f$ with the property that every planar graph $G$ with maximum degree $d$ admits a drawing with noncrossing straight-line edges, using…
A drawing of a graph in the plane is {\it pseudolinear} if the edges of the drawing can be extended to doubly-infinite curves that form an arrangement of pseudolines, that is, any pair of edges crosses precisely once. A special case are…
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,…