36 citations · 44 across the 9 of their papers we have counts for
9 papers
Primitive path homology
Jingyan Li, Yuri Muranov, Jie Wu +1
In this paper we introduce a primitive path homology theory on the category of simple digraphs. On the subcategory of asymmetric digraphs, this theory coincides with the path homol…
Homology of graph burnings
Yuri Muranov, Anna Muranova
In this paper we study graph burnings using methods of algebraic topology. We prove that the time function of a burning is a graph map to a path graph. Afterwards, we define a cate…
On Cubical Sets of Quivers and Digraphs
Rolando Jimenez, Vladimir Vershinin, Yuri Muranov
The singular cubical homology theory for the category of quivers or digraphs can be constructed similarly to the classical singular homology theory for topological spaces. The case…
Path homology of directed hypergraphs
Yuri Muranov, Anna Szczepkowska, Vladimir Vershinin
We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. A…
Homotopy theory for digraphs
Alexander Grigor'yan, Yong Lin, Yuri Muranov +1
We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors i…
Homologies of path complexes and digraphs
Alexander Grigor'yan, Yong Lin, Yuri Muranov +1
In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes f…