Hamiltonicity, minimum degree and leaf number

Article

DOI: 10.1007/s10474-017-0716-4

Cite this article as:
Mafuta, P., Mukwembi, S., Munyira, S. et al. Acta Math. Hungar. (2017) 152: 217. doi:10.1007/s10474-017-0716-4
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Abstract

We prove a new sufficient condition for a connected graph to be Hamiltonian in terms of the leaf number and the minimum degree. Our results give solutions to conjectures on the Hamiltonicity and traceability of graphs. We considerably generalize known results in the area by showing that if G is a connected graph having minimum degree \({\delta}\) and leaf number L such that \({\delta \ge \frac{L}{2}+1}\), then G is Hamiltonian and thus traceable.

Key words and phrases

Hamiltonicity traceability minimum degree leaf number 

Mathematics Subject Classification

05C45 05C35 05C05 

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  • P. Mafuta
    • 1
  • S. Mukwembi
    • 1
    • 2
  • S. Munyira
    • 1
  • T. Vetrík
    • 3
  1. 1.Department of MathematicsUniversity of ZimbabweHarareZimbabwe
  2. 2.School of Mathematics, Statistics and Computer ScienceUniversity of KwaZulu-NatalDurbanSouth Africa
  3. 3.Department of Mathematics and Applied MathematicsUniversity of the Free StateBloemfonteinSouth Africa

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