There are several graph $NP$-complete problems that have sub-exponential time algorithm on planar graph instances. What is the fastest algorithm for HC problem on cubic planar graphs? Is there a sub-exponential algorithm for this class of graphs?
Sub-exponential algorithm for Hamiltonian cycle problem on cubic planar graphs?
ds.algorithms;graph theory
Planar separators easily give an $n^{O(\sqrt{n})}$ algorithm. This can be improved to $2^{O(\sqrt{n})}$ which is optimal (up to the constant in the exponent) for general planar graphs assuming ETH. I am not sure if being cubic helps or not. 