No-Rainbow Problem and the Surjective Constraint Satisfaction Problem
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Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints. In this paper we show that one of the most popular variants of the SCSP, called No-Rainbow Problem, is NP-Hard. Additionally, we disprove the conjecture saying that SCSP over a constraint language Γ is equivalent to CSP over the same language with constants. Our counter example also shows that the complexity of SCSP cannot be described in terms of polymorphisms of the constraint language.
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