4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles

Carsten Thomassen, Carol T. Zamfirescu

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Abstract

We prove that there exists an infinite family of 4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles. We do not know whether there exists such a family of 5-regular 5-connected Hamiltonian graphs.
Original languageEnglish
JournalAustralasian Journal of Combinatorics
Volume81
Issue number2
Pages (from-to)334–338
ISSN1034-4942
Publication statusPublished - 2021

Keywords

  • Hamiltonian cycle
  • Regular graph

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