5 papers
Homotopy classification of closed polygonal lines
E. Alkin, O. Nikitenko, A. Skopenkov
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is do…
Low rank matrix completion and realization of graphs: results and problems
S. Dzhenzher, T. Garaev, O. Nikitenko +3
The Netflix problem (from machine learning) asks the following. Given a ratings matrix in which each entry represents the rating of movie by customer , if customer $…
Invariants of almost embeddings of graphs in the plane: results and problems
E. Alkin, E. Bordacheva, A. Miroshnikov +2
A graph drawing in the plane is called an almost embedding if images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. We introduce integer invariants of alm…
Cycles in graphs and in hypergraphs: towards homology theory
A. Miroshnikov, O. Nikitenko, A. Skopenkov
In this expository paper we present some ideas of algebraic topology (more precisely, of homology theory) in a language accessible to non-specialists in the area. A -cycle in a…
Cycles in graphs and in hypergraphs: results and problems
E. Alkin, S. Dzhenzher, O. Nikitenko +2
This is an expository paper. A -cycle in a graph is a set of edges such that every vertex is contained in an even number of edges from . E.g., a cycle in the sense of gra…