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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Bibliographic Details
Main Authors: Y.M. Borse, A.V. Sonawane, S.R. Shaikh
Format: Article
Language:English
Published: Taylor & Francis Group 2019-12-01
Series:AKCE International Journal of Graphs and Combinatorics
Online Access:http://www.sciencedirect.com/science/article/pii/S0972860017301500
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Summary: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
ISSN:0972-8600