2024/04/22 by A. Miroshnikov, Miroshnikov, A., O. Nikitenko +3
Computer Science · #05-01 #05C38 #05C65 #55-01 #55R80 #55S15 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #History and Overview (math.HO) #Scientific Research and Philosophical Inquiry
paper · pdf · doi:10.48550/arxiv.2406.16705
openalex publication_date 2024/04/22 · openalex created_date 2024/06/26 · openalex updated_date 2026/07/28
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 1-cycle in a graph is a set C of edges such that every vertex is contained in an even number of edges from C. It is easy to check that the sum (modulo 2) of 1-cycles is a 1-cycle. We start from the following problems: to find \bullet the number of all 1-cycles in a given graph; \bullet a small number of 1-cycles in a given graph such that any 1-cycle is the sum of some of them. We consider generalizations (of these problems) to graphs with symmetry, to 2-cycles in 2-dimensional hypergraphs, and to certain configuration spaces of graphs (namely, to the square and the deleted square).