Hamilton cycle rich 2-factorization of complete bipartite graphs
| Autor: | Appu Muthusamy, R. Sangeetha |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Discrete Mathematics, Algorithms and Applications. :1550026 |
| ISSN: | 1793-8317 1793-8309 |
| DOI: | 10.1142/s1793830915500263 |
| Popis: | A 2-factorization {F1, F2,…,Fd} of a 2d-regular graph G such that each [Formula: see text] and the remaining Fi's are all Hamilton cycles is called Hamilton cycle rich 2-factorization of G, where Gi's are the given non-isomorphic 2-factors of G. In this paper, we prove that there exists a 2-factorization {F1, F2,…,Fn} of K2n,2n such that F1 ≅ G1, F2 ≅ G2 and the remaining Fi's are Hamilton cycles of K2n,2n, where G1 and G2 are the given two non-isomorphic 2-factors of K2n,2n. In fact our result together with the earlier results settles the existence of Hamilton cycle rich 2-factorizations of K(m, p), the complete p-partite graph with m vertices in each partite set, except when (m, p) = (2n + 1, 2), in the case that two of the 2-factors are isomorphic to the given two non-isomorphic 2-factors and the remaining are Hamilton cycles. |
| Databáze: | OpenAIRE |
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