# Pairs of forbidden class of subgraphs concerning ${K}_{1,3}$ and P₆ to have a cycle containing specified vertices

Takeshi Sugiyama; Masao Tsugaki

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 3, page 645-650
- ISSN: 2083-5892

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topTakeshi Sugiyama, and Masao Tsugaki. "Pairs of forbidden class of subgraphs concerning $K_{1,3}$ and P₆ to have a cycle containing specified vertices." Discussiones Mathematicae Graph Theory 29.3 (2009): 645-650. <http://eudml.org/doc/271054>.

@article{TakeshiSugiyama2009,

abstract = {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.},

author = {Takeshi Sugiyama, Masao Tsugaki},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {forbidden subgraph; cycle},

language = {eng},

number = {3},

pages = {645-650},

title = {Pairs of forbidden class of subgraphs concerning $K_\{1,3\}$ and P₆ to have a cycle containing specified vertices},

url = {http://eudml.org/doc/271054},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Takeshi Sugiyama

AU - Masao Tsugaki

TI - Pairs of forbidden class of subgraphs concerning $K_{1,3}$ and P₆ to have a cycle containing specified vertices

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 3

SP - 645

EP - 650

AB - 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.

LA - eng

KW - forbidden subgraph; cycle

UR - http://eudml.org/doc/271054

ER -

## References

top- [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. Zbl0883.05089
- [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. Zbl0879.05050
- [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. Zbl1158.05036
- [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. Zbl0838.05071
- [6] T. Sugiyama, Forbidden subgraphs and existence of cycles passing through specified vertices, in preparation. Zbl1158.05036