NP–HARD PROBLEMS NATURALLY ARISING IN KNOT THEORY

Abstract

We prove that certain problems naturally arising in knot theory are NP–hard or NP–complete. These are the problems of obtaining one dia-gram from another one of a link in a bounded number of Reidemeister moves, determining whether a link has an unlinking or splitting number k, finding a k-component unlink as a sublink, and finding a k-component alternating sublink.