Miller, Jonathan; Naimi, Ramin An algorithm for detecting intrinsically knotted graphs. (English) Zbl 1291.57005 Exp. Math. 23, No. 1, 6-12 (2014). 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. Cited in 4 Documents 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 Keywords:spatial graph; intrinsically knotted; Arf invariant; linking number Citations:Zbl 1292.05091 PDFBibTeX XMLCite \textit{J. Miller} and \textit{R. Naimi}, Exp. Math. 23, No. 1, 6--12 (2014; Zbl 1291.57005) Full Text: DOI arXiv References: [1] DOI: 10.1002/jgt.3190070410 · Zbl 0524.05028 · doi:10.1002/jgt.3190070410 [2] DOI: 10.1002/jgt.10017 · Zbl 1176.05022 · doi:10.1002/jgt.10017 [3] DOI: 10.1002/jgt.10114 · Zbl 1022.05019 · doi:10.1002/jgt.10114 [4] Goldberg N. [Goldberg et al. 14], To appear in Algebraic and Geometric Topology (2014) [5] Kohara T. [Kohara and Suzuki 92], Knots 90 (Osaka, 1990) pp 435– (1992) [6] DOI: 10.1006/jctb.1995.1006 · Zbl 0823.05038 · doi:10.1006/jctb.1995.1006 [7] DOI: 10.1016/j.jctb.2004.08.001 · Zbl 1061.05088 · doi:10.1016/j.jctb.2004.08.001 [8] DOI: 10.1006/jctb.1995.1032 · Zbl 0832.05032 · doi:10.1006/jctb.1995.1032 [9] DOI: 10.1016/S0166-8641(99)00228-X · Zbl 0968.57001 · doi:10.1016/S0166-8641(99)00228-X [10] DOI: 10.1016/j.jctb.2008.10.002 · Zbl 1179.05110 · doi:10.1016/j.jctb.2008.10.002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.