Toward a Theory of Planarity: Hanani-Tutte and Planarity Variants - Schaefer, Marcus (Journal of Graph Algorithms and Applications, 2013)
We study Hanani-Tutte style theorems for various notions of planarity, including partially embedded planarity and simultaneous planarity. This approach brings together the combinatorial, computational and algebraic aspects of planarity notions and may serve as a uniform foundation for planarity, as suggested earlier in the writings of Tutte and Wu.