An Algorithm for Detecting Intrinsically Knotted Graphs

Abstract

We describe an algorithm that recognizes some (possibly all) intrinsically knotted (IK) graphs and can help find knotless embeddings for graphs that are not IK. The algorithm, implemented as a Mathematica program, has already been used in [Goldberg et al. 14] to greatly expand the list of known minor minimal IK graphs and to find knotless embeddings for some graphs that had previously resisted attempts to classify them as IK or non-IK.

2000 AMS Subject Classification:

• 57M15
• 57M25
• 05C10

Keywords:

• spatial graph
• intrinsically knotted
• Arf invariant
• linking number