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- W4385774611 abstract "This is an expository paper. 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 $C$. E.g., a cycle in the sense of graph theory is a $1$-cycle, but not vice versa. It is easy to check that the sum (modulo $2$) of $1$-cycles is a $1$-cycle. In this text we study 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 also consider generalizations (of these problems) to graphs with symmetry, and to $2$-cycles in $2$-dimensional hypergraphs." @default.
- W4385774611 created "2023-08-12" @default.
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- W4385774611 date "2023-08-09" @default.
- W4385774611 modified "2023-09-27" @default.
- W4385774611 title "Cycles in graphs and in hypergraphs" @default.
- W4385774611 doi "https://doi.org/10.48550/arxiv.2308.05175" @default.
- W4385774611 hasPublicationYear "2023" @default.
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