Factorizations of the product of cycles
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 C1,C2,…,Cnwith |Ci|=2ki≥4 for each i. El-Zanati and Eynden proved that G has a C-factorization,...
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Taylor & Francis Group
2019-12-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0972860017301500 |
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doaj-5d7f104f2a914a1eb3e8bef69d1ac0ab2020-11-25T03:04:44ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002019-12-01163324331Factorizations of the product of cyclesY.M. Borse0A.V. Sonawane1S.R. Shaikh2Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, IndiaCorresponding author.; Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, IndiaDepartment of Mathematics, Savitribai Phule Pune University, Pune 411 007, IndiaAn 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 C1,C2,…,Cnwith |Ci|=2ki≥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=2twith 2≤t≤k1+k2+⋯+kn. We extend this result to get factorizations of G into m-regular, m-connected and bipancyclic subgraphs. We prove that for 2≤m<2n, 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 2n and s=2twith m≤t≤k1+k2+⋯+kn. Keywords: Cycle product, Factorization, n-connected, Regular, Bipancyclichttp://www.sciencedirect.com/science/article/pii/S0972860017301500 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Y.M. Borse A.V. Sonawane S.R. Shaikh |
| spellingShingle |
Y.M. Borse A.V. Sonawane S.R. Shaikh Factorizations of the product of cycles AKCE International Journal of Graphs and Combinatorics |
| author_facet |
Y.M. Borse A.V. Sonawane S.R. Shaikh |
| author_sort |
Y.M. Borse |
| title |
Factorizations of the product of cycles |
| title_short |
Factorizations of the product of cycles |
| title_full |
Factorizations of the product of cycles |
| title_fullStr |
Factorizations of the product of cycles |
| title_full_unstemmed |
Factorizations of the product of cycles |
| title_sort |
factorizations of the product of cycles |
| publisher |
Taylor & Francis Group |
| series |
AKCE International Journal of Graphs and Combinatorics |
| issn |
0972-8600 |
| publishDate |
2019-12-01 |
| description |
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 C1,C2,…,Cnwith |Ci|=2ki≥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=2twith 2≤t≤k1+k2+⋯+kn. We extend this result to get factorizations of G into m-regular, m-connected and bipancyclic subgraphs. We prove that for 2≤m<2n, 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 2n and s=2twith m≤t≤k1+k2+⋯+kn. Keywords: Cycle product, Factorization, n-connected, Regular, Bipancyclic |
| url |
http://www.sciencedirect.com/science/article/pii/S0972860017301500 |
| work_keys_str_mv |
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