Related papers: Connes embeddability of graph products
In this paper we investigate the connectedness and the isomorphism problems for zig-zag products of two graphs. A sufficient condition for the zig-zag product of two graphs to be connected is provided, reducing to the study of the…
We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension - also known as the Stefan problem with Gibbs-Thomson correction.
In this short note we prove Hilbert--Schmidt stability for graph products of abelian groups and $C^*$-algebras on chordal graphs. In particular, this shows that right-angled Artin groups on chordal graphs are Hilbert--Schmidt stable.
Embedding large graphs in low dimensional spaces has recently attracted significant interest due to its wide applications such as graph visualization, link prediction and node classification. Existing methods focus on computing the…
The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of "pattern graphs" can be embedded into a given graph $H$ (that is, is isomorphic to a…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
We analyse the geometric instability of embeddings produced by graph neural networks (GNNs). Existing methods are only applicable for small graphs and lack context in the graph domain. We propose a simple, efficient and graph-native Graph…
Graph is an important data representation ubiquitously existing in the real world. However, analyzing the graph data is computationally difficult due to its non-Euclidean nature. Graph embedding is a powerful tool to solve the graph…
We prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous to the fact that…
A set of colored graphs are compatible, if for every color $i$, the number of vertices of color $i$ is the same in every graph. A simultaneous embedding of $k$ compatibly colored graphs, each with $n$ vertices, consists of $k$ planar…
We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each vertex in G can be reached by an infinite…
In this paper, we give new, tight subexponential lower bounds for a number of graph embedding problems. We introduce two related combinatorial problems, which we call String Crafting and Orthogonal Vector crafting, and show that these…
We extend the classical stability theorem of Erdos and Simonovits for forbidden graphs of logarithmic order.
Given a hereditary graph property $\mathcal{P}$, consider distributions of random orderings of vertices of graphs $G\in\mathcal{P}$ that are preserved under isomorphisms and under taking induced subgraphs. We show that for many properties…
Recent graph neural networks (GNN) has achieved remarkable performance in node representation learning. One key factor of GNN's success is the \emph{smoothness} property on node representations. Despite this, most GNN models are fragile to…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
We study the stability of the embeddability of compact 2-concave CR manifolds in complex manifolds under small horizontal perturbations of the CR structure.
A graph is called normal if its vertex set can be covered by cliques and also by stable sets, such that every such clique and stable set have non-empty intersection. This notion is due to Korner, who introduced the class of normal graphs as…