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We construct for all    k  ∈  N    a  k ‐edge‐connected digraph  D  with    s  ,  t  ∈  V  (  D  )    such that there are no edge‐disjoint    s  →  t    and    t  →  s    paths. We use in our construction “self‐similar” graphs which technique could be useful in other problems as well.

Highly Connected Infinite Digraphs Without Edge‐Disjoint Back and Forth Paths Between a Certain Vertex Pair