相关论文: Axis-Parallel Right Angle Crossing Graphs

We study algorithms for drawing planar graphs and 1-planar graphs using cubic B\'ezier curves with bounded curvature. We show that any n-vertex 1-planar graph has a 1-planar RAC drawing using a single cubic B\'ezier curve per edge, and this…

A graph $G$ is a link-irregular graph if every two distinct vertices of $G$ have non-isomorphic links. The link of a vertex $v$ in $G$ is the subgraph induced by the neighbors of $v$ in $G$. Ali, Chartrand and Zhang [Discussiones…

We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…

Reeb graphs are simple topological descriptors with applications in many areas like topological data analysis and computational geometry. Despite their prevalence, visualization of Reeb graphs has received less attention. In this paper, we…

A drawing of a graph in the plane is a thrackle if every pair of edges intersects exactly once, either at a common vertex or at a proper crossing. Conway's conjecture states that a thrackle has at most as many edges as vertices. In this…

Unit edge-length drawings, rectilinear drawings (where each edge is either a horizontal or a vertical segment), and rectangular face drawings are among the most studied subjects in Graph Drawing. However, most of the literature on these…

A k-distance r-coloring of a graph is a coloring of the vertices of the graph such that if the distance between 2 vertices x and y is less or equal to k, then x and y must have distinct colors. A planar graph is a graph that can be drawn…

In this paper we present a characterisation, by an infinite family of minimal forbidden induced subgraphs, of proper circular arc graphs which are intersection graphs of paths on a grid, where each path has at most one bend (turn).

Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes.…

A partial edge drawing (PED) of a graph is a variation of a node-link diagram. PED draws a link, which is a partial visual representation of an edge, and reduces visual clutter of the node-link diagram. However, more time is required to…

Recent studies show that graph neural networks (GNNs) are vulnerable to backdoor attacks. Existing backdoor attacks against GNNs use fixed-pattern triggers and lack reasonable trigger constraints, overlooking individual graph…

Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph…

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…

A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative…

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex $u$ is represented by a geometric object $R(u)$ and in which each edge $(u,v)$ is represented…

We define and study a class of graphs, called 2-stab interval graphs (2SIG), with boxicity 2 which properly contains the class of interval graphs. A 2SIG is an axes-parallel rectangle intersection graph where the rectangles have unit height…

Graph anomaly detection (GAD) is a vital task in graph-based machine learning and has been widely applied in many real-world applications. The primary goal of GAD is to capture anomalous nodes from graph datasets, which evidently deviate…

We study a question that lies at the intersection of classical research subjects in Topological Graph Theory and Graph Drawing: Computing a drawing of a graph with a prescribed number of crossings on a given set $S$ of points, while…

A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two cross exactly once. A drawing of a graph is pseudolinear if…