  Vertex splitting replaces a vertex by two copies and partitions its incident
edges amongst the copies. This problem has been studied as a graph editing
operation to achieve desired properties with as few splits as possible, most
often planarity, for which the problem is NP-hard. Here we study how to
minimize the number of splits to turn a plane graph into an outerplane one. We
tackle this problem by establishing a direct connection between splitting a
plane graph to outerplanarity, finding a connected face cover, and finding a
feedback vertex set in its dual. We prove NP-completeness for plane biconnected
graphs, while we show that a polynomial-time algorithm exists for maximal
planar graphs. Finally, we provide upper and lower bounds for certain families
of maximal planar graphs.
