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Jul 14, 2023 at 12:43 comment added Jens Fischer Thank you for the construction. Effectively, it does not work in this generality. I am going to look into the other direction now, what I can say about a graph, who has such a separator and is $r$-regular.
Jul 4, 2023 at 9:29 history answered Martin Tancer CC BY-SA 4.0