3 citations · 11 across the 13 of their papers we have counts for
13 papers
Biregular bipartite labeled multigraphs and perfect matchings in bipartite tensor products
Ilya I. Bogdanov, Fedor Petrov, Anton Sadovnichiy +1
In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulat…
On forest and bipartite cuts in sparse graphs
Ilya I. Bogdanov, Elizaveta Neustroeva, Georgy Sokolov +3
The paper is devoted to sufficient conditions for the existence of vertex cuts in simple graphs, where the induced subgraph on the cut vertices belongs to a specified graph class.…
The continualization approach to the on-line hypergraph coloring
Margarita Akhmejanova, Ilya Bogdanov, Grigory Chelnokov
The paper deals with an algorithmic problem concerning combinatorial game theory. Here we introduce and analyze a continuous generalization of Chip Game from the work of Duraj, Gut…
Covering three-tori with cubes
Ilya Bogdanov, Oleg Grigoryan, Maksim Zhukovskii
Let be the minimum number of cubes of side needed to cover the unit three-torus . We prove new lower and upper bounds for…
Feynman checkers: the probability of direction reversal
Ilya Bogdanov
We study the most elementary model of electron motion introduced by R.Feynman in 1965. It is a game, in which a checker moves on a checkerboard by simple rules, and we count the tu…
Algebraic proofs of linear versions of the Conway--Gordon--Sachs theorem and the van Kampen--Flores theorem
Ilya I. Bogdanov, Alexander D. Matushkin
In this paper we present short algebraic proofs of the Linear Conway--Gordon--Sachs and the Linear van Kampen--Flores theorems in the spirit of the Radon theorem on convex hulls. {…
Solvability of cubic and quartic equations using one radical
Danil Akhtyamov, Ilya Bogdanov
Theorem. An irreducible cubic polynomial with rational coefficients has a root in a one step radical extension of Q if and only if the discriminate is a square of a rational number…
Number of vertices in graphs with locally small chromatic number and large chromatic number
Ilya I. Bogdanov
We discuss the minimal number of vertices in a graph with a large chromatic number such that each ball of a fixed radius in it has a small chromatic number. It is shown that for ev…
Examples of topologically highly chromatic graphs with locally small chromatic number
Ilya I. Bogdanov
Kierstead, Szemerédi, and Trotter showed that a graph with at most vertices such that each ball of radius in it is -colorable should have chromatic…
The maximal length of the period of a periodic word defined by restrictions
Ilya I. Bogdanov, Grigory R. Chelnokov
We determine the maximal length of the period of a periodic word defined by restrictions. It happens to be the corresponding Fibonacci number.
On graphs with a large chromatic number containing no small odd cycles
Sergey L. Berlov, Ilya I. Bogdanov
In this paper, we present the lower bounds for the number of vertices in a graph with a large chromatic number containing no small odd cycles.
Finding a subset of nonnegative vectors with a coordinatewise large sum
Ilya I. Bogdanov, Grigory R. Chelnokov
Given a rational and nonnegative -dimensional real vectors , ..., , we show that it is always possible to choose of them su…
Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits
Ilya I. Bogdanov, Karine G. Kuyumzhiyan
Let G be an exceptional simple algebraic group, and let T be a maximal torus in G. In this paper, for every such G, we find all simple rational G-modules V with the following prope…