Related papers: Bratteli--Vershik models and graph covering models
We introduce a general framework for leveraging graph stream data for temporal prediction-based applications. Our proposed framework includes novel methods for learning an appropriate graph time-series representation, modeling and weighting…
Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are $\rm W[1]$-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including…
There has been a growing excitement that implicit graph generative models could be used to design or discover new molecules for medicine or material design. Because these molecules have not been discovered, they naturally lie in unexplored…
Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…
We study a class of simple dimension groups in which the cyclic subgroup generated by the order unit is replaced by a copy of $\mathbb{Z}^{2}$ satisfying some strict conditions. Our main results are necessary and sufficient conditions on a…
We study the Lebwohl-Lasher model for systems in which spin are arranged on random graph lattices. At equilibrium our analysis follows the theory of spin-systems on random graphs which allows us to derive exact bifurcation conditions for…
The weak cop number of infinite graphs can be seen as a coarse-geometric analogue to the cop number of finite graphs. We show that every vertex transitive graph with at least one thick end has infinite weak cop number. It follows that every…
We study the dynamics of homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker cosmological models with positive spatial curvature within the context of mimetic gravity theory by employing dynamical system techniques. Our analysis…
We call an oriented odd cycle alternating if it has exactly one vertex whose in-degree and out-degree are both positive. In this paper, we investigate whether certain graphs admit an orientation that avoids alternating odd cycles as…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
We study the complexity of the following related computational tasks concerning a fixed countable graph G: 1. Does a countable graph H provided as input have a(n induced) subgraph isomorphic to G? 2. Given a countable graph H that has a(n…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
In this paper, we study sequences of perfect t-embeddings of a uniformly weighted family of graphs we call generalized tower graphs. We show that the embeddings of these graphs satisfy certain technical assumptions, in particular, the…
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…
We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when…
In the context of the chromatic-number problem, a critical graph is an instance where the deletion of any element would decrease the graph's chromatic number. Such instances have shown to be interesting objects of study for deepen the…
The Szemer\'edi Regularity Lemma, in combination with the Blow-up Lemma, form the Regularity Method, a fundamental tool in graph embeddings, albeit restricted to very large and dense graphs. We propose an alternative vertex-partitioning…
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…
In the Feedback Vertex Set problem, we aim to find a small set $S$ of vertices in a graph intersecting every cycle. The Subset Feedback Vertex Set problem requires $S$ to intersect only those cycles that include a vertex of some specified…