Related papers: Discrimination of Graph Isomorphism Classes by Con…
We study a family of graph modification problems called the F-Vertex Splitting problem. Given a graph G, the task is to determine whether G can be transformed into a graph G-prime belonging to a graph class F through a sequence of at most k…
Real-world graphs are complex to process for performing effective analysis, such as anomaly detection. However, recently, there have been several research efforts addressing the issues surrounding graph-based anomaly detection. In this…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…
A popular way to define or characterize graph classes is via forbidden subgraphs or forbidden minors. These characterizations play a key role in graph theory, but they rarely lead to efficient algorithms to recognize these classes. In…
Unigraphs are graphs uniquely determined by their own degree sequence up to isomorphism. There are many subclasses of unigraphs such as threshold graphs, split matrogenic graphs, matroidal graphs, and matrogenic graphs. Unigraphs and these…
Anomaly detection is a crucial task in complex distributed systems. A thorough understanding of the requirements and challenges of anomaly detection is pivotal to the security of such systems, especially for real-world deployment. While…
A classical difficult isomorphism testing problem is to test isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. It is known that this problem can be reduced to solving the alternating matrix space…
Graph generative models become increasingly effective for data distribution approximation and data augmentation. While they have aroused public concerns about their malicious misuses or misinformation broadcasts, just as what Deepfake…
The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
Graph Isomorphism is one of the classical problems of graph theory for which no deterministic polynomial-time algorithm is currently known, but has been neither proven to be NP-complete. Several heuristic algorithms have been proposed to…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
Intersection graphs are well-studied in the area of graph algorithms. Some intersection graph classes are known to have algorithms enumerating all unlabeled graphs by reverse search. Since these algorithms output graphs one by one and the…
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…
To determine that two given undirected graphs are isomorphic, we construct for them auxiliary graphs, using the breadth-first search. This makes capability to position vertices in each digraph with respect to each other. If the given graphs…
In this note we prove that every closed graph $G$ is up to isomorphism a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graph recognition.
Omnidirectional cameras are widely used in such areas as robotics and virtual reality as they provide a wide field of view. Their images are often processed with classical methods, which might unfortunately lead to non-optimal solutions as…