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Abstrakty
In [3], Faudree and Gould showed that if a 2-connected graph contains no $K_{1,3}$ and P₆ as an induced subgraph, then the graph is hamiltonian. In this paper, we consider the extension of this result to cycles passing through specified vertices. We define the families of graphs which are extension of the forbidden pair $K_{1,3}$ and P₆, and prove that the forbidden families implies the existence of cycles passing through specified vertices.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
645-650
Opis fizyczny
Daty
wydano
2009
otrzymano
2008-02-04
poprawiono
2009-01-02
zaakceptowano
2009-03-10
Twórcy
autor
- Department of Mathematics, Keio University, Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan
autor
- Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
Bibliografia
- [1] H. Broersma, H. Li, J. Li, F. Tian and H.J. Veldman, Cycles through subsets with large degree sums, Discrete Math. 171 (1997) 43-54, doi: 10.1016/S0012-365X(96)00071-4.
- [2] R. Diestel, Graph Theory, second edition (New York, Springer, 2000).
- [3] R. Faudree and R. Gould, Characterizing forbidden pairs for hamiltonian properties, Discrete Math. 173 (1997) 45-60, doi: 10.1016/S0012-365X(96)00147-1.
- [4] J. Fujisawa, K. Ota, T. Sugiyama and M. Tsugaki, Forbidden subgraphs and existence of paths and cycles passing through specified vertices, Discrete Math. 308 (2008) 6111-6114, doi: 10.1016/j.disc.2007.11.033.
- [5] K. Ota, Cycles through prescribed vertices with large degree sum, Discrete Math. 145 (1995) 201-210, doi: 10.1016/0012-365X(94)00036-I.
- [6] T. Sugiyama, Forbidden subgraphs and existence of cycles passing through specified vertices, in preparation.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1470