Anna A. Taranenko

activity

20172021

collaborators

6 papers

math.CO2021

On a metric property of perfect colorings

Anna A. Taranenko

Given a perfect coloring of a graph, we prove that the $L_{1}$ distance between two rows of the adjacency matrix of the graph is not less than the $L_{1}$ distance between the correspo…

math.CO2019

Perfect 2-colorings of Hamming graphs

Evgeny A. Bespalov, Denis S. Krotov, Aleksandr A. Matiushev +2

We consider the problem of existence of perfect $2$ -colorings (equitable $2$ -partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs a…

math.CO2019

Regularity and counting lemmas for multidimensional matrices

Anna A. Taranenko

In the present paper we propose generalizations of the regularity and counting lemmas for multidimensional matrices under a finite alphabet. Firstly, we prove a variant of a multid…

math.CO2019

Algebraic properties of perfect structures

Anna A. Taranenko

A perfect structure is a triple $(M, P, S)$ of matrices $M, P$ and $S$ of consistent sizes such that $M P = P S$ . Perfect structures comprise similar matrices, eigenvectors, perfect co…

math.CO2018

On the König-Hall-Egerváry theorem for multidimensional matrices and multipartite hypergraphs

Anna A. Taranenko

One of possible interpretations of the well-known König--Hall--Egerváry theorem is a full characterization of all bipartite graphs extremal for fractional matchings of a given weig…

math.CO2017

Transversals, plexes, and multiplexes in iterated quasigroups

Anna Taranenko

A $d$ -ary quasigroup of order $n$ is a $d$ -ary operation over a set of cardinality $n$ such that the Cayley table of the operation is a $d$ -dimensional latin hypercube of the same…