Hamiltonian cycles in n-factor-critical graphs

Ken Ichi Kawarabayashi, Katsuhiro Ota, Akira Saito

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)71-82
Number of pages12
JournalDiscrete Mathematics
Volume240
Issue number1-3
DOIs
Publication statusPublished - 2001 Sep 28

Keywords

  • Degree sum
  • Factor-critical graphs
  • Hamiltonian cycle
  • Toughness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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