NP-hard problems naturally arising in knot theory

TL;DR

This paper demonstrates that several computational problems in knot theory, such as diagram transformation and unlinking number determination, are NP-hard or NP-complete, highlighting their computational complexity.

Contribution

It establishes the NP-hardness and NP-completeness of key problems in knot theory, connecting topological questions with computational complexity.

Findings

Proves diagram transformation problem is NP-hard.

Shows unlinking and splitting number problems are NP-complete.

Identifies complexity of finding specific sublinks in knots.

Abstract

We prove that certain problems naturally arising in knot theory are NP--hard or NP--complete. These are the problems of obtaining one diagram 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.