Hamiltonian cycles in n-factor-critical graphs

Ken Ichi Kawarabayashi, Katsuhiro Ota, Akira Saito

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)71-82
ページ数12
ジャーナルDiscrete Mathematics
240
1-3
DOI
出版ステータスPublished - 2001 9月 28

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 離散数学と組合せ数学

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