Conditions on subgraphs, degrees, and domination for hamiltonian properties of graphs

Wei Zheng, Hajo Broersma, Ligong Wang*, Shenggui Zhang

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Motivated by a hamiltonicity result due to Ageev, involving claw-free graphs with a small domination number, we study analogous conditions that guarantee different types of hamiltonian properties. In our first main result we relax the condition on claw-freeness and obtain a common generalization of the result of Ageev and a recent result due to Cai. Our other results deal with similar conditions that guarantee traceability, pancyclicity and hamiltonian-connectivity. We also leave some open problems.
Original languageEnglish
Article number111644
JournalDiscrete mathematics
Volume343
Issue number1
DOIs
Publication statusPublished - Jan 2020

Keywords

  • Claw-free graph
  • Implicit claw-heavy
  • Dominating set
  • Hamiltonian property

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