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KNOTS AND LINKS IN LINEAR EMBEDDINGS OF K6

  • Published : 2007.05.31

Abstract

We investigate the number of knots and links in linear embeddings of $K_6$, the complete graph with 6 vertices. Concretely, we show that any linear embedding of $K_6$ contains either only one Hopf link, or three Hopf links and one trefoil knot.

Keywords

References

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  5. Linearly embedded graphs in 3–space with homotopically free exteriors vol.15, pp.2, 2015, https://doi.org/10.2140/agt.2015.15.1161
  6. Classification of book representations of K6 2017, https://doi.org/10.1142/S0218216517500754
  7. HEPTAGONAL KNOTS AND RADON PARTITIONS vol.48, pp.2, 2011, https://doi.org/10.4134/JKMS.2011.48.2.367
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  9. A refinement of the Conway–Gordon theorems vol.156, pp.17, 2009, https://doi.org/10.1016/j.topol.2009.08.013
  10. LINKING IN STRAIGHT-EDGE EMBEDDINGS OF K7 vol.19, pp.11, 2010, https://doi.org/10.1142/S0218216510008467
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