Degree conditions on claws and modified claws for hamiltonicity of graphs

Jun Fujisawa, Tomoki Yamashita

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Ore presented a degree condition involving every pair of nonadjacent vertices for a graph to be hamiltonian. Fan [New sufficient conditions for cycles in graphs, J. Combin. Theory Ser. B 37 (1984) 221-227] showed that not all the pairs of nonadjacent vertices are required, but only the pairs of vertices at the distance two suffice. Bedrossian et al. [A generalization of Fan's condition for hamiltonicity, pancyclicity, and hamiltonian connectedness, Discrete Math. 115 (1993) 39-50] improved Fan's result involving the pairs of vertices contained in an induced claw or an induced modified claw. On the other hand, Matthews and Sumner [Longest paths and cycles in K1, 3-free graphs, J. Graph Theory 9 (1985) 269-277] gave a minimum degree condition for a claw-free graph to be hamiltonian. In this paper, we give a new degree condition in an induced claw or an induced modified claw ensuring the hamiltonicity of graphs which extends both results of Bederossian et al. and Matthews and Sumner.

Original languageEnglish
Pages (from-to)1612-1619
Number of pages8
JournalDiscrete Mathematics
Volume308
Issue number9
DOIs
Publication statusPublished - 2008 May 6

Keywords

  • Claw
  • Claw-free
  • Degree condition
  • Hamiltonian cycle
  • Modified claw

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'Degree conditions on claws and modified claws for hamiltonicity of graphs'. Together they form a unique fingerprint.

  • Cite this