All NP problems can be reduced to NP-Complete problems, can an NP-Complete problem be reduced to a NP problem (non complete)?

  • $\begingroup$ Are you asking whether, for a given NP-complete problem $NP_C$ there exists any problem $NP_x \in NP, NP_x \ne NP_C$ such that $NP_C$ can be reduced to $NP_x$? That would make $NP_C$ NP-complete, too. And yes, there is more than one NP-complete problem. (Or no, such an $NP_x$ is not non-complete.) $\endgroup$
    – greybeard
    May 20, 2023 at 16:18

1 Answer 1


An NP-complete problem is in NP, by definition. No reduction needed.

  • 1
    $\begingroup$ Okay I feel really dumb now! Thanks for making it clear $\endgroup$ Aug 1, 2020 at 3:57
  • 2
    $\begingroup$ @PedroPapel Welcome to Computer Science! please consider accepting this as the answer if it helped you, thank you. $\endgroup$
    – Evil
    Aug 2, 2020 at 23:38

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