Related papers: Connectivity for matroids based on rough sets
Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic…
Fleischner introduced the idea of splitting a vertex of degree at least three in a connected graph and used the operation to characterize Eulerian graphs. Raghunathan et. al. extended the splitting operation from graphs to binary matroids.…
The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics. Many hard computational problems on graphs turn out to be efficiently solvable in…
We show that an adjoint of a loopless matroid is connected if and only if it itself is connected. Our first goal is to study the adjoint of modular matroids. We prove that a modular matroid has only one adjoint (up to isomorphism) which can…
Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
We introduce the concept of matching connectivity as a notion of connectivity in graph admitting perfect matchings which heavily relies on the structural properties of those matchings. We generalise a result of Robertson, Seymour and Thomas…
Matrix factorization models have been extensively studied as a valuable test-bed for understanding the implicit biases of overparameterized models. Although both low nuclear norm and low rank regularization have been studied for these…
Physical and functional constraints on biological networks lead to complex topological patterns across multiple scales in their organization. A particular type of higher-order network feature that has received considerable interest is…
An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair. For pairs for which neither matroid can be obtained, up to isomorphism, from the other…
A generalised notion of connection on a fibre bundle E over a manifold M is presented. These connections are characterised by a smooth distribution on E which projects onto a (not necessarily integrable) distribution on M and which, in…
In this article, we investigate the multi-parametric matroid problem. The weights of the elements of the matroid's ground set depend linearly on an arbitrary but fixed number of parameters, each of which is taken from a real interval. The…
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…
In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some relationship between Laplacian matrix and resistance…
Let $M$ be a representable matroid, and $Q, R, S, T$ subsets of the ground set. We prove that, if $M$ is sufficiently large, then there is an element $e$ such that deleting or contracting $e$ preserves both the $Q$-$R$ and the $S$-$T$…
A connected covering is a design system in which the corresponding {\em block graph} is connected. The minimum size of such coverings are called {\em connected coverings numbers}. In this paper, we present various formulas and bounds for…
Fiber graphs of Gr\"obner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The connectivity of the graphs has implications…
The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…
Connectivity is a fundamental property of quantum graphs, previously studied in the operator system model for matrix quantum graphs and via graph homomorphisms in the quantum adjacency matrix model. In this paper, we develop an algebraic…
A matroid $N$ is said to be triangle-rounded in a class of matroids $\mathcal{M}$ if each $3$-connected matroid $M\in \mathcal{M}$ with a triangle $T$ and an $N$-minor has an $N$-minor with $T$ as triangle. Reid gave a result useful to…