TY - JOUR
T1 - Quadrangularly connected claw-free graphs
AU - Li, Ming Chu
AU - Guo, Cheng
AU - Xiong, Liming
AU - Li, Dengxin
AU - Lai, Hong Jian
PY - 2007/5/6
Y1 - 2007/5/6
N2 - A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E (G), G has a sequence of l-cycles (3 ≤ l ≤ 4)C1, C2, ..., Cr such that e1 ∈ E (C1) and e2 ∈ E (Cr) and E (Ci) ∩ E (Ci + 1) ≠ ∅ for i = 1, 2, ..., r - 1. In this paper, we show that every quadrangularly connected claw-free graph without vertices of degree 1, which does not contain an induced subgraph H isomorphic to either G1 or G2 such that N1 (x, G) of every vertex x of degree 4 in H is disconnected is hamiltonian, which implies a result by Z. Ryjáček [Hamiltonian circuits in N2-locally connected K1, 3-free graphs, J. Graph Theory 14 (1990) 321-331] and other known results.
AB - A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E (G), G has a sequence of l-cycles (3 ≤ l ≤ 4)C1, C2, ..., Cr such that e1 ∈ E (C1) and e2 ∈ E (Cr) and E (Ci) ∩ E (Ci + 1) ≠ ∅ for i = 1, 2, ..., r - 1. In this paper, we show that every quadrangularly connected claw-free graph without vertices of degree 1, which does not contain an induced subgraph H isomorphic to either G1 or G2 such that N1 (x, G) of every vertex x of degree 4 in H is disconnected is hamiltonian, which implies a result by Z. Ryjáček [Hamiltonian circuits in N2-locally connected K1, 3-free graphs, J. Graph Theory 14 (1990) 321-331] and other known results.
KW - Claw-free graph
KW - Cycle
KW - Quadrangularly connected
UR - https://www.scopus.com/pages/publications/33846781369
U2 - 10.1016/j.disc.2006.07.034
DO - 10.1016/j.disc.2006.07.034
M3 - Article
AN - SCOPUS:33846781369
SN - 0012-365X
VL - 307
SP - 1205
EP - 1211
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 9-10
ER -