@article{Gronemann_Nöllenburg_Villedieu_2024, title={Splitting Plane Graphs to Outerplanarity}, volume={28}, url={https://jgaa.info/index.php/jgaa/article/view/2970}, DOI={10.7155/jgaa.v28i3.2970}, abstractNote={<p>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.<br />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. Additionally, we show upper and lower bounds for certain families of maximal planar graphs. Finally, we provide a SAT formulation for the problem, and evaluate it on a small benchmark.</p>}, number={3}, journal={Journal of Graph Algorithms and Applications}, author={Gronemann, Martin and Nöllenburg, Martin and Villedieu, Anaïs}, year={2024}, month={Sep.}, pages={31–48} }