Complexity of the min-max (regret) versions of min cut problems

This paper investigates the complexity of the min-max and min-max regret versions of the min s-t cut and min cut problems. Even if the underlying problems are closely related and both polynomial, the complexity of their min-max and min-max regret versions, for a constant number of scenarios, is quite contrasted since they are respectively strongly NP hard and polynomial. However, for a non constant number of scenarios, these versions become strongly NP -hard for both problems. In the interval scenario case, min-max versions are trivially polynomial. Moreover, for min-max regret versions, we obtain the same contrasted result as for a constant number of scenarios: min-max regret min s-t cut is strongly NP -hard whereas min-max regret min cut is polynomial.