A is a graph, ad B is A's subgraph by deleting an edge of A. Proving forward is easy, but how can we prove backward?
How can we prove a graph is planar iff its subgraph is planar?
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graph-theory
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0If this were true, there would be an easy proof that every graph was planar: just keep deleting edges until none are left. – 2017-02-17
2 Answers
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Specifically, consider this graph, which is the complete graph on 5 nodes with a single edge removed. It is planar, as the image shows; but famously the complete graph on 5 nodes is not planar.
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but how can we prove backward?
We cannot, because then any graph can be shown to be planar, and that's obviously not the case.