TY - JOUR
T1 - A note on 3-connected hourglass-free claw-free Hamilton-connected graphs
AU - Liu, Xia
AU - Xiong, Liming
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/8
Y1 - 2022/8
N2 - An hourglass Γ0 is the graph with degree sequence (4, 2, 2, 2, 2) and a claw is the bipartite complete graph K1,3. In this paper, we show that (1) every 3-connected, essentially 4-connected {K1,3,Γ0}-free graph is Hamilton-connected, (2) every 3-connected {K1,3,Γ0,P16}-free graph is Hamilton-connected, where (1) improves similar results of (Li et al. (2008) [11]) and hence (Broersma et al. (2001) [4]); (2) settles one conjecture posed in (Ryjáček et al. (2018) [18]).
AB - An hourglass Γ0 is the graph with degree sequence (4, 2, 2, 2, 2) and a claw is the bipartite complete graph K1,3. In this paper, we show that (1) every 3-connected, essentially 4-connected {K1,3,Γ0}-free graph is Hamilton-connected, (2) every 3-connected {K1,3,Γ0,P16}-free graph is Hamilton-connected, where (1) improves similar results of (Li et al. (2008) [11]) and hence (Broersma et al. (2001) [4]); (2) settles one conjecture posed in (Ryjáček et al. (2018) [18]).
KW - Hamilton-connected
KW - Hourglass-free
KW - Line graph
KW - SM-closure
KW - Strongly spanning trailable
UR - http://www.scopus.com/inward/record.url?scp=85127196633&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2022.112910
DO - 10.1016/j.disc.2022.112910
M3 - Article
AN - SCOPUS:85127196633
SN - 0012-365X
VL - 345
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 8
M1 - 112910
ER -