4-regular 4-connected Hamiltonian graphs with few Hamiltonian cycles

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 if there exists such a family of 5-regular 5-connected Hamiltonian graphs.

4 pages, 3 figures

References in corpus (1)

• Graphs with few Hamiltonian Cycles