Related papers: Simpler and Unified Recognition Algorithm for Path…
We investigate the parameterized complexity of the recognition problem for the proper $H$-graphs. The $H$-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph $H$, and the properness means that the…
It was noted already in the 90s that many classic graph classes, such as interval, chordal, and bipartite graphs, can be characterized by the existence of an ordering of the vertices avoiding some ordered subgraphs, called patterns. Very…
We consider the worst-case query complexity of some variants of certain \cl{PPAD}-complete search problems. Suppose we are given a graph $G$ and a vertex $s \in V(G)$. We denote the directed graph obtained from $G$ by directing all edges in…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely:…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…
Node classification is one of the hottest tasks in graph analysis. Though existing studies have explored various node representations in directed and undirected graphs, they have overlooked the distinctions of their capabilities to capture…
Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation,…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
Graphs are ubiquitous in encoding relational information of real-world objects in many domains. Graph generation, whose purpose is to generate new graphs from a distribution similar to the observed graphs, has received increasing attention…
Pathways are integral to systems biology. Their classical representation has proven useful but is inconsistent in the meaning assigned to each arrow (or edge) and inadvertently implies the isolation of one pathway from another. Conversely,…
In this paper we consider Contact graphs of Paths on a Grid (CPG graphs), i.e. graphs for which there exists a family of interiorly disjoint paths on a grid in one-to-one correspondence with their vertex set such that two vertices are…
Let $P(G)=(P_{0}(G),P_{1}(G),\cdots, P_{\rho}(G))$ be the path sequence of a graph $G$, where $P_{i}(G)$ is the number of paths with length $i$ and $\rho$ is the length of a longest path in $G$. In this paper, we first give the path…
We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, the so called $B_0$-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a polynomial time…