Splitting Plane Graphs to Outerplanarity

Martin Gronemann; Martin Nöllenburg; Anaïs Villedieu

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arXiv · 2301.09440

Splitting Plane Graphs to Outerplanarity

Martin Gronemann·Martin Nöllenburg·Anaïs Villedieu

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Abstract

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.

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Martin Gronemann, Martin Nöllenburg, Anaïs Villedieu. 2023-01-23. Splitting Plane Graphs to Outerplanarity. https://arxiv.org/abs/2301.09440

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