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An algorithm for detecting intrinsically knotted graphs. (English) Zbl 1291.57005

Summary: 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 [N. Goldberg, T. W. Mattman and R. Naimi, Algebr. Geom. Topol. 14, No. 3, 1801–1823 (2014; Zbl 1292.05091)] 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.

MSC:

57M15 Relations of low-dimensional topology with graph theory
57M25 Knots and links in the \(3\)-sphere (MSC2010)
05C10 Planar graphs; geometric and topological aspects of graph theory

Citations:

Zbl 1292.05091
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References:

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