TY - JOUR
T1 - Forbidden subgraphs and the existence of paths and cycles passing through specified vertices
AU - Fujisawa, Jun
AU - Ota, Katsuhiro
AU - Sugiyama, Takeshi
AU - Tsugaki, Masao
PY - 2008/12/28
Y1 - 2008/12/28
N2 - In [H. Broersma, H. Li, J. Li, F. Tian, H.J. Veldman, Cycles through subsets with large degree sums, Discrete Math. 171 (1997) 43-54], Duffus et al. showed that every connected graph G which contains no induced subgraph isomorphic to a claw or a net is traceable. They also showed that if a 2-connected graph G satisfies the above conditions, then G is hamiltonian. In this paper, modifying the conditions of Duffus et al.'s theorems, we give forbidden structures for a specified set of vertices which assures the existence of paths and cycles passing through these vertices.
AB - In [H. Broersma, H. Li, J. Li, F. Tian, H.J. Veldman, Cycles through subsets with large degree sums, Discrete Math. 171 (1997) 43-54], Duffus et al. showed that every connected graph G which contains no induced subgraph isomorphic to a claw or a net is traceable. They also showed that if a 2-connected graph G satisfies the above conditions, then G is hamiltonian. In this paper, modifying the conditions of Duffus et al.'s theorems, we give forbidden structures for a specified set of vertices which assures the existence of paths and cycles passing through these vertices.
KW - Forbidden subgraphs cycle
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U2 - 10.1016/j.disc.2007.11.033
DO - 10.1016/j.disc.2007.11.033
M3 - Article
AN - SCOPUS:56649114288
VL - 308
SP - 6111
EP - 6114
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 24
ER -