2 problems

Hamiltonicity conjecture. Every connected bicirculant, except for the complete graph $K_2$ and the generalized Petersen graphs $G(m,2)$ with

Bicirculant Hamiltonicity conjecture. Every connected bicirculant, except for $K_2$ and the generalized Petersen graphs $G(m,2)$ with $m\equiv 5\pmod 6$, is hamiltonian.