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Jul 31 at 15:49 comment added Felix Schröder There is a standard terminology: Homotopic parallel edges are defined to not have any vertices in the bounded components they leave after removing the closed curve obtained by concatenating them. If you are on the sphere instead of the plane you would say that one component contains all vertices. So what you describe are pairwise homotopic parallel edges.
Jul 29 at 20:45 answer added user533847 timeline score: 3
Jul 29 at 19:30 history edited Hao S CC BY-SA 4.0
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Jul 29 at 17:33 history asked Hao S CC BY-SA 4.0