TY - JOUR
T1 - Hamilton-connected properties of 3-connected {claw,hourglass,bull}-free graphs
AU - Wang, Panpan
AU - Xiong, Liming
N1 - Publisher Copyright:
© 2024 The Author(s).
PY - 2024
Y1 - 2024
N2 - An hourglass Γ0 is the graph with degree sequence {4, 2, 2, 2, 2}. In this paper, for integers j ≥ i ≥ 1, the bull Bi,j is the graph obtained by attaching endvertices of two disjoint paths of lengths i, j to two vertices of a triangle. We show that every 3-connected {K1,3, Γ0, X}free graph, where X ∈ {B2,12, B4,10, B6,8}, is Hamilton-connected. Moreover, we give an example to show the sharpness of our result, and complete the characterization of forbidden induced bulls implying Hamilton-connectedness of a 3-connected {claw, hourglass, bull}-free graph.
AB - An hourglass Γ0 is the graph with degree sequence {4, 2, 2, 2, 2}. In this paper, for integers j ≥ i ≥ 1, the bull Bi,j is the graph obtained by attaching endvertices of two disjoint paths of lengths i, j to two vertices of a triangle. We show that every 3-connected {K1,3, Γ0, X}free graph, where X ∈ {B2,12, B4,10, B6,8}, is Hamilton-connected. Moreover, we give an example to show the sharpness of our result, and complete the characterization of forbidden induced bulls implying Hamilton-connectedness of a 3-connected {claw, hourglass, bull}-free graph.
KW - Bull
KW - Claw
KW - Forbidden subgraph
KW - Hamilton-connected
KW - Hourglass
UR - http://www.scopus.com/inward/record.url?scp=85216884528&partnerID=8YFLogxK
U2 - 10.61091/ars161-15
DO - 10.61091/ars161-15
M3 - Article
AN - SCOPUS:85216884528
SN - 0381-7032
VL - 161
SP - 187
EP - 209
JO - Ars Combinatoria
JF - Ars Combinatoria
ER -