Given a graph G I want to find the maximum planar subgraph which is a grid graph. (Because the nodes of this subgraph represent points on a grid).
Is there any library in python for finding the maximum planar subgraph?
Is there some way how to implement these constraints for the grid graph?
Edit: As I understood I am looking for the maximum planar subgraph which is at most 4-connected and at least 2-connected
I doubt there are any implementations for the algorithms you are looking for.
The problem, also known as Planar Edge Deletion, Edge Planarization, Graph Planarization, or sometimes Minimum Planarization, is NP-complete and was shown in 2007 to be fixed-parameter tractable (for every fixed number of edges you want to delete, there is a "linear time algorithm" for the problem). However, the algorithm is extremely non-trivial and rely on deep mathematical results.
* K. Kawarabayashi and B.A. Reed. Computing crossing number in linear time. In: Proc. STOC 2007, 382—390.
This doesn't answer your question about your particular problem, but you can find theory for a related problem involving grids by searching for "bidimensionality".
It's the idea that every graph is either low treewidth or contains a large grid minor which makes it possible to get solution in polynomial time.
See Section 3 in Beyond Planar Graphs presentation by DeMaine. Also this is mentioned in Section 1 of Width parameters beyond tree-width and their applications, which is a good tutorial for the basics needed to understand bidimensionality results.
