Could you non-deterministically "guess" the correct Hamiltonian path in logspace, keeping track of the current vertex (log(n) bits) and a count of how many vertices you've visited (log(n) bits)?
Does that mean finding a Hamiltonian path is NL?
(This is too simple; what is my mistake?)
A Hamiltonian path is a path that visits all vertices in a graph. The concept exists for directed and undirected graphs.