Pairs of forbidden class of subgraphs concerning 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
Access Full Article
top
Abstract
topHow to cite
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
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.