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math.CO2021
4-regular 4-connected Hamiltonian graphs with few Hamiltonian cycles
Carsten Thomassen, Carol T. Zamfirescu
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 if there exists such a family…
math.CO2021
Regular graphs with few longest cycles
Carol T. Zamfirescu
Motivated by work of Haythorpe, Thomassen and the author showed that there exists a positive constant such that there is an infinite family of 4-regular 4-connected graphs, eac…