# Haythorpe, Michael

## Almost all non-Hamiltonian 3-regular graphs are 1-connected ★★

Author(s): Haythorpe

\begin{conjecture} Denote by $NH(n)$ the number of non-Hamiltonian 3-regular graphs of size $2n$, and similarly denote by $NHB(n)$ the number of non-Hamiltonian 3-regular 1-connected graphs of size $2n$.

Is it true that $\lim\limits_{n \rightarrow \infty} \displaystyle\frac{NHB(n)}{NH(n)} = 1$? \end{conjecture}