I have the following problem to solve: Given a set of sequences of edges of an undirected, planar, connected graph, find a "reasonable" reconstruction of the graph. There is an unknown number of vertices in the graph, but it's given that each edge in each given sequence shares a vertex with the edge next to it in the sequence. We could further assume, that all the sequences start with the same edge.

Ideally, I would need an algorithm to reconstruct the graph.

Has such problem been already studied or does anyone see a way to transform it to another known problem? So far, I can only think of genetic algorithms.