Input: Planar graph $G$ and its embedding in sphere $\Pi$, edges $e, f \in E(G)$ and integer $k$.Output: The set of closed walks in $G$ using $e$ and $f$ which contains $k$ faces of $G$. In other words the set of close walks in $G$ via $e$ and $f$ which each one partition $\Pi$ into two set of faces which one is of size $k$.I'm wondering if this problem is solvable in poly-time!
Closed Walk in Planar Graphs
algorithms;graph theory