Hamiltonian, Bridge, 3-regular, 1-connected


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}

Keywords: Hamiltonian, Bridge, 3-regular, 1-connected

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