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- W2809562705 abstract "Abstract An H -factorization of a graph G is a partition of the edge set of G into spanning subgraphs (or factors) each of whose components are isomorphic to a graph H . Let G be the Cartesian product of the cycles C 1 , C 2 , … , C n with | C i | = 2 k i ≥ 4 for each i . El-Zanati and Eynden proved that G has a C -factorization, where C is a cycle of length s , if and only if s = 2 t with 2 ≤ t ≤ k 1 + k 2 + ⋯ + k n . We extend this result to get factorizations of G into m -regular, m -connected and bipancyclic subgraphs. We prove that for 2 ≤ m 2 n , the graph G has an H -factorization, where H is an m -regular, m -connected and bipancyclic graph on s vertices, if and only if m divides 2 n and s = 2 t with m ≤ t ≤ k 1 + k 2 + ⋯ + k n ." @default.
- W2809562705 created "2018-06-29" @default.
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- W2809562705 date "2019-12-01" @default.
- W2809562705 modified "2023-10-04" @default.
- W2809562705 title "Factorizations of the product of cycles" @default.
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- W2809562705 doi "https://doi.org/10.1016/j.akcej.2018.06.003" @default.
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