TY - JOUR
T1 - Hamiltonian cycles in n-factor-critical graphs
AU - Kawarabayashi, Ken Ichi
AU - Ota, Katsuhiro
AU - Saito, Akira
N1 - Funding Information:
∗Corresponding author. E-mail addresses: k keniti@comb.math.keio.ac.jp (K. Kawarabayashi), ohta@comb.math.kevo.ac.jp (K. Ota), asaito@am.chs.nihon-u.ac.jp (A. Saito). 1Partially supported by Research Fellowships of the Japan Society fo r the Promotion of Science fo r Young Scientists.
PY - 2001/9/28
Y1 - 2001/9/28
N2 - A graph G is said to be n-factor-critical if G - S has a 1-factor for any S ⊂ V(G) with |S| = n. In this paper, we prove that if G is a 2-connected n-factor-critical graph of order p with σ33/2(G)≥(p - n - 1), then G is hamiltonian with some exceptions. To extend this theorem, we define a (k,n)-factor-critical graph to be a graph G such that G - S has a k-factor for any S ⊂ V(G) with |S| = n. We conjecture that if G is a 2-connected (k,n)-factor-critical graph of order p with σ3(G)≥3/2(p - n - k), then G is hamiltonian with some exceptions. In this paper, we characterize all such graphs that satisfy the assumption, but are not 1-tough. Using this, we verify the conjecture for k≤2.
AB - A graph G is said to be n-factor-critical if G - S has a 1-factor for any S ⊂ V(G) with |S| = n. In this paper, we prove that if G is a 2-connected n-factor-critical graph of order p with σ33/2(G)≥(p - n - 1), then G is hamiltonian with some exceptions. To extend this theorem, we define a (k,n)-factor-critical graph to be a graph G such that G - S has a k-factor for any S ⊂ V(G) with |S| = n. We conjecture that if G is a 2-connected (k,n)-factor-critical graph of order p with σ3(G)≥3/2(p - n - k), then G is hamiltonian with some exceptions. In this paper, we characterize all such graphs that satisfy the assumption, but are not 1-tough. Using this, we verify the conjecture for k≤2.
KW - Degree sum
KW - Factor-critical graphs
KW - Hamiltonian cycle
KW - Toughness
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U2 - 10.1016/S0012-365X(00)00386-1
DO - 10.1016/S0012-365X(00)00386-1
M3 - Article
AN - SCOPUS:0035964595
SN - 0012-365X
VL - 240
SP - 71
EP - 82
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1-3
ER -