Related papers: Drawing Reeb Graphs
We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph $G$ with two distinct terminal vertices and two positive integers $p$ and $k$, the question is…
Motivated by cognitive experiments providing evidence that large crossing-angles do not impair the readability of a graph drawing, RAC (Right Angle Crossing) drawings were introduced to address the problem of producing readable…
We present algorithms and experiments for the visualization of directed graphs that focus on displaying their reachability information. Our algorithms are based on the concepts of the path and channel decomposition as proposed in the…
We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every edge…
Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in…
Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known…
We consider the problem of covering a graph with a given number of induced subgraphs so that the maximum number of vertices in each subgraph is minimized. We prove NP-completeness of the problem, prove lower bounds, and give approximation…
Graphs are typically visualized as node-link diagrams. Although there is a fair amount of research focusing on crossing minimization to improve readability, little attention has been paid on how to handle crossings when they are an…
Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and studies geometric representations of non-planar graphs in terms of forbidden crossing configurations. Aim of this survey is to describe the main research…
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.…
Graphs are essential representations in the professions and education concerning the science, technology, engineering, and mathematics (STEM) disciplines. Beyond their academic relevance, graphs find extensive utility in everyday scenarios,…
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Graph drawing addresses the problem of finding a layout of a graph that satisfies given aesthetic and understandability objectives. The most important objective in graph drawing is minimization of the number of crossings in the drawing, as…
Graph neural networks have been successful in many learning problems and real-world applications. A recent line of research explores the power of graph neural networks to solve combinatorial and graph algorithmic problems such as subgraph…
In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly $90^\circ$, where the number of bends on such polylines is typically restricted in some way.…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines…
It is well known that any graph admits a crossing-free straight-line drawing in $\mathbb{R}^3$ and that any planar graph admits the same even in $\mathbb{R}^2$. For a graph $G$ and $d \in \{2,3\}$, let $\rho^1_d(G)$ denote the smallest…
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…