Using this algorithm, we were able to generate complete lists of hypohamiltonian graphs of much larger orders than what was previously possible. This allowed us amongst others to find the smallest hypohamiltonian graph of girth 6 and to show that the smallest planar hypohamiltonian graph has order at least 23.
This is joint work with Carol Zamfirescu.
We show that if $V(G)| = n$, then the $n$-Bell colour graph of $G$
is Hamiltonian unless $G \cong K_n, K_n-e$.
We also show that for $k \geq 4$, the $k$-Stirling colour graph of a tree with at
least $k+1$ vertices is Hamiltonian.