Geodesic
Pairs of forbidden class of subgraphs concerning $K_{1,3}$ and P₆ to have a cycle containing specified vertices
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 645-650.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: forbidden subgraph, cycle 
@article{DMGT_2009_29_3_a13,
     author = {Sugiyama, Takeshi and Tsugaki, Masao},
     title = {Pairs of forbidden class of subgraphs concerning $K_{1,3}$ and {P₆} to have a cycle containing specified vertices},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {645--650},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a13/}
}
TY  - JOUR
AU  - Sugiyama, Takeshi
AU  - Tsugaki, Masao
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
SP  - 645
EP  - 650
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a13/
LA  - en
ID  - DMGT_2009_29_3_a13
ER  - 
%0 Journal Article
%A Sugiyama, Takeshi
%A Tsugaki, Masao
%T Pairs of forbidden class of subgraphs concerning $K_{1,3}$ and P₆ to have a cycle containing specified vertices
%J Discussiones Mathematicae. Graph Theory
%D 2009
%P 645-650
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a13/
%G en
%F DMGT_2009_29_3_a13
Sugiyama, Takeshi; Tsugaki, Masao. Pairs of forbidden class of subgraphs concerning $K_{1,3}$ and P₆ to have a cycle containing specified vertices. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 645-650. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a13/

[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.