Doubly stochastic matrices and dicycle covers and packings in eulerian digraphs

on the Integral Dicycle Packings and Covers and the Linear ordering Polytope

The linear ordering polytope P~.o is defined as the convex hull of all the incidence vectors of the acyclic tournaments on n nodes, it is known that for every facet of P~.o there corresponds a digraph inducing it. Let D be a digraph that induces a facet-defining inequality for P~.o, that is nonequivalent to a trivial inequality or to a 3-dicycle inequality. We show that for such a digraph the f...

Transversal Packings and Covers

Vertex degrees and doubly stochastic graph matrices

In this article, the relationship between vertex degrees and entries of the doubly stochastic graph matrix has been investigated. In particular, we present an upper bound for the main diagonal entries of a doubly stochastic graphmatrix and investigate the relations between a kind of distance for graph vertices and the vertex degrees. These results are used to answer in negative Merris’ question...

Generalized Doubly Stochastic Matrices and Linear Preservers

A real or complex n × n matrix is generalized doubly stochastic if all of its row sums and column sums equal one. Denote by V the linear space spanned by such matrices. We study the reducibility of V under the group Γ of linear operators of the form A 7→ PAQ, where P and Q are n×n permutation matrices. Using this result, we show that every linear operator φ : V → V mapping the set of generalize...

Directed graphs, Hamiltonicity and doubly stochastic matrices

We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled)Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)-entry of the fundamental matrices of the Markov chains induced by the same policies. In particular, we focus on the subset of these policies that induce doubly stochastic probability tran...