4-regular 4-connected Hamiltonian graphs with few Hamiltonian cycles
Combinatorics
2025-06-13 v1
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.
Keywords
Cite
@article{arxiv.2104.06347,
title = {4-regular 4-connected Hamiltonian graphs with few Hamiltonian cycles},
author = {Carsten Thomassen and Carol T. Zamfirescu},
journal= {arXiv preprint arXiv:2104.06347},
year = {2025}
}
Comments
4 pages, 3 figures