Related papers: Regularity inheritance in hypergraphs
Spectral hypergraph sparsification, a natural generalization of the well-studied spectral sparsification notion on graphs, has been the subject of intensive research in recent years. In this work, we consider spectral hypergraph…
In this article we study higher homological properties of $n$-levelled algebras and connect them to properties of the underlying graphs. Notably, to each $2$-representation-finite quadratic monomial algebra $\Lambda$ we associate a…
In this paper, we introduce a method called graph fusion embedding, designed for multi-graph embedding with shared vertex sets. Under the framework of supervised learning, our method exhibits a remarkable and highly desirable synergistic…
The sparse representation classifier (SRC) is shown to work well for image recognition problems that satisfy a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the…
We consider the problem of partitioning a graph into a non-fixed number of non-overlapping subgraphs of maximum density. The density of a partition is the sum of the densities of the subgraphs, where the density of a subgraph is its average…
Recently, a number of variants of the notion of cut-preserving hypergraph sparsification have been studied in the literature. These variants include directed hypergraph sparsification, submodular hypergraph sparsification, general notions…
Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are often in irregular form, which makes them more…
Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…
Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have…
We study the existence and regularity of invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relative partial hyperbolicity on non-trivial and…
We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
What distribution of graphical degree sequence is invariant under ``scaling''? Are these graphs always power-law graphs? We show the answer is a surprising ``yes'' for sparse graphs if we ignore isolated vertices, or more generally, the…
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise…
We show that the Ramsey number is linear for every uniform hypergraph with bounded-degree. This is a hypergraph extension of the famous theorem for ordinary graphs which Chv\'atal et al. showed in 1983. Our proof is simple, contains the…