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Hopefully improving the question
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Can any non-planar graph be 'translated' towith n minimum crossing points be 'drawn' on a sphere so so the vertice and edge sets are the same yetand it has noa connected subset A with minimum r crossing points on the sphereand a disjoint connected subset B with minimum s crossing points where r+s=n? And other subsets can be found for any value r such that 1 < r < n ?

Can any non-planar graph be 'translated' to a sphere so the vertice and edge sets are the same yet it has no crossing points on the sphere?

Can any non-planar graph with n minimum crossing points be 'drawn' on a sphere so the vertice and edge sets are the same and it has a connected subset A with minimum r crossing points and a disjoint connected subset B with minimum s crossing points where r+s=n? And other subsets can be found for any value r such that 1 < r < n ?

Post Closed as "Not suitable for this site" by Stefan Kohl, Gerry Myerson, Noah Schweber, Tony Huynh, Andreas Blass
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About planar graphs?

Can any non-planar graph be 'translated' to a sphere so the vertice and edge sets are the same yet it has no crossing points on the sphere?