I have a planar graph $G$ consisting of the edges and vertices $(E,V)$. And so, there are $C=E-V+1$ faces in total. The graph is given as a list of edges.
The question is, how to find the edges that don't lie on the faces of the graph? One way I can think of is to find the spanning tree of the graph, use the non-spanning-tree edges to complete the faces, and get all the edges on the faces. Since we already have the on-face edges, we can obtain the not-on-face edges by subtracting the on-face edges from the all the edges.
But is there a more direct way of doing this?