相关论文: Combinatorial Characterization of the Assur Graphs…
We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed…
This work is a study of the properties of collaboration networks employing the formalism of weighted graphs to represent their one-mode projection. The weight of the edges is directly the number of times that a partnership has been…
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of…
Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…
In here, I present a series of combinatorial equalities derived using a graph based approach. Different nodes in the graphs are visited following probabilistic dynamics of a moving dot. The results are presented in such a way that the…
Recently Baranyai described a necessary combinatorial characterisation of graph rigidity for dimension 3. In this short note we provide a counter-example to the converse of the condition. Additionally, we provide an alternative proof to the…
In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
We revisit the concept of minimal rigidity as applied to soft repulsive, frictionless sphere packings in two-dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's…
In this paper, we provide a unified definition of mediated graph, a combinatorial structure with multiple applications in mathematical optimization. We study some geometric and algebraic properties of this family of graphs and analyze…
One-dimensional atomic mixtures of fermions can effectively realize spin chains and thus constitute a clean and controllable platform to study quantum magnetism. Such strongly correlated quantum systems are also of sustained interest to…
We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…
Functional structures from across the engineered and biological world combine rigid elements such as bones and columns with flexible ones such as cables, fibers and membranes. These structures are known loosely as tensegrities, since these…
Current paper introduces a Hypergraph Graph model of data storage which can be represented as a hybrid data structure based on Hypergraph and Graph. The pro-posed data structure is claimed to realize complex combinatorial structures. The…
We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature…
This paper introduces assume/guarantee contracts on continuous-time control systems, hereby extending contract theories for discrete systems to certain new model classes and specifications. Contracts are regarded as formal characterizations…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…