Cycles in graphs and in hypergraphs (in Russian)
<|reference_start|>Cycles in graphs and in hypergraphs (in Russian): In this expository paper we present some ideas of algebraic topology 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).<|reference_end|>
@article{dzhenzher2024cycles,
    title={Cycles in graphs and in hypergraphs (in Russian)},
    author={S. Dzhenzher, A. Miroshnikov, O. Nikitenko, A. Skopenkov},
    journal={arXiv preprint arXiv:2406.16705},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.16705},
    primaryClass={math.HO cs.DM}
}