Their claim is: > Conjecture. There is no polynomial time algorithm for deciding <some problem>. […] [A variant of the problem] is NP-complete. […] Theorem 2.

Their claim is: > Conjecture. There is no polynomial time algorithm for deciding <some problem>. […] [A variant of the problem] is NP-complete. […] Theorem 2. There is a constructive algorithm for deciding [the variant problem]. The number of basic steps to do this [is bounded by something that is, I think, intended to be polynomial, although there is a hidden exponent of k and a direct exponent of n]. I don’t see any justification or source for the statement that the variant problem is actually NP-complete. Even if their proof was correct, wouldn’t it just disprove a conjecture?