Definition of NP-complete in English:

NP-complete

adjective

Computing Mathematics
  • Designating a member of a class of complex and intractable NP problems which can be converted into any other problem of the same class, such that if an algorithm for its solution in polynomial time existed, it would be possible to solve all NP problems in polynomial time; (of a problem) both NP and NP-hard.

Origin

1970s.