Do you think this definition of homeomorphism in graph theory correct?

"Two graphs are homeomorphic if they become isomorphic when all vertices of degree 2 are removed."

PS: 1) I have not seen this definition anywhere else but I can't 100% claim that somebody else did not use it. 2) I hope it's not correct, because otherwise homeomorphism is usually made out to be much harder than it actually is by other definitions!

  • $\begingroup$ How do you remove all vertices from a circle graph? Also, if you are interested in simple graphs, your definition has the problem that it may leave that realm $\endgroup$ – Hagen von Eitzen May 1 at 13:02
  • $\begingroup$ For a circle graph, of course both compared graphs would be null as a result of this process, and null graphs are isomorphic(I think). Can you give an example to the second problem you mentioned? $\endgroup$ – AKubilay May 1 at 19:22

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