does everyone know, if there already exists a definition of subgraphs, which do not contain a "hole"?
EDITED: That means: I presuppose a planar embedding of a graph G and I want to find a connected subgraph G', so that the subgraph do not surrounds any other node of the graph G \ G' in the given embedding. So it is a kind of "convex" subgraph. For example, if G' is cycle-free it would be such a subgraph.
Thanks a lot! Benjamin