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Planar Graphs

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Here is a simple statement which I've yet to prove satisfactorily:

 

Adding/deleting loops, parallel edges and edges in series does not affect the planarity of a graph.

 

If a graph is planar, then removing anything from it does not create any edge crossings, so the graph remains planar. If a graph is not planar, then adding anything to it will or will not create any edge crosssings, so the graph remains unplanar.

 

Now I have to show that adding (removing) loops, parallel edges and edges in series does not affect the planarity of a(n) planar (unplanar respectively) graph. This is were I stopped. I'm trying to think of a good argument which shows that a planar graph remains planar after the addition of loops. I'm guessing I'll have to describe a process that can add loops without creating edge crossings. Any tips?

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