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 -