TY - JOUR
T1 - Forbidden pairs for 2-factorable and hamiltonian graphs under the necessary condition
AU - Wang, Qiang
AU - Xiong, Liming
N1 - Publisher Copyright:
© 2025 Elsevier B.V.
PY - 2025/10/15
Y1 - 2025/10/15
N2 - In [1], Wang and Xiong characterize all forbidden pairs (not necessary connected) R,S such that 2-connected {R,S}-free graph G admitting a 2-factor is hamiltonian. To be more comprehensive, in this paper, we characterize all forbidden pairs (not necessary connected) R,S such that connected (or 2-edge-connected) {R,S}-free graph G admitting a 2-factor is hamiltonian. Besides, we characterize all forbidden pairs (not necessary connected) R,S such that connected (or 2-edge-connected) {R,S}-free graph G admitting an even-factor has a 2-factor. Comparing with the main result of Yang and Xiong (2023), we give all disconnected forbidden pairs. In the end, we find all forbidden pairs R,S such that connected (or 2-edge-connected) {R,S}-free graph G who has an even-factor is hamiltonian.
AB - In [1], Wang and Xiong characterize all forbidden pairs (not necessary connected) R,S such that 2-connected {R,S}-free graph G admitting a 2-factor is hamiltonian. To be more comprehensive, in this paper, we characterize all forbidden pairs (not necessary connected) R,S such that connected (or 2-edge-connected) {R,S}-free graph G admitting a 2-factor is hamiltonian. Besides, we characterize all forbidden pairs (not necessary connected) R,S such that connected (or 2-edge-connected) {R,S}-free graph G admitting an even-factor has a 2-factor. Comparing with the main result of Yang and Xiong (2023), we give all disconnected forbidden pairs. In the end, we find all forbidden pairs R,S such that connected (or 2-edge-connected) {R,S}-free graph G who has an even-factor is hamiltonian.
KW - 2-factor
KW - Even-factor
KW - Forbidden pair
KW - Hamiltonian
UR - http://www.scopus.com/inward/record.url?scp=105005090658&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2025.05.017
DO - 10.1016/j.dam.2025.05.017
M3 - Article
AN - SCOPUS:105005090658
SN - 0166-218X
VL - 373
SP - 290
EP - 300
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -