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

Fingerprint

Claw
Degree Condition
Hamiltonians
Hamiltonicity
Fans
Graph in graph theory
Graph theory
Pancyclicity
Long Cycle
Claw-free Graphs
Ores
Longest Path
Connectedness
Minimum Degree
Cycle
Sufficient Conditions

Keywords

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Degree conditions on claws and modified claws for hamiltonicity of graphs. / Fujisawa, Jun; Yamashita, Tomoki.

In: Discrete Mathematics, Vol. 308, No. 9, 06.05.2008, p. 1612-1619.

Research output: Contribution to journalArticle

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