Swap Planarity, a puzzle where adjacent vertices swap locations, is NP-complete to solve, and minimizing swaps for trees is NP-complete, though any solvable instance needs only O(n-squared) swaps.
On embedding an outer-planar graph in a point set
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Geometry and Generation of a New Graph Planarity Game
Swap Planarity, a puzzle where adjacent vertices swap locations, is NP-complete to solve, and minimizing swaps for trees is NP-complete, though any solvable instance needs only O(n-squared) swaps.