4 papers
On winding numbers of almost embeddings of in the plane
Emil Alkin, Alexander Miroshnikov
Let be the complete graph on four vertices. Let be a continuous map of to the plane such that -images of non-adjacent edges are disjoint. For any vertex $v \in K…
Invariants of almost embeddings of graphs in the plane
E. Alkin, A. Miroshnikov, A. Skopenkov
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely,…
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…