Problem: I am looking for an algorithm which finds all vertices that are adjacent to exterior region of a planar graph(For a planar graph, any region=face can be considered as the exterior region /face).
Attempt: Using the planarity check algorithm, an algorithm can be constructed with polynomial bound.
Questions: My questions are-
Are there any literature /algorithms regarding the problem?
Can the problem have a log-space time algorithm (without using planarity check algorithm)?
Motivation: Trying to find the outer cycle of a planar graph quickly to reduce the complexity of Hamiltonian circuit problem.