SOME RESULTS ON INTRINSICALLY KNOTTED GRAPHS

DOI Web Site 2 Citations
  • PAUL BLAIN
    Department of Mathematics, University of Washington, seattle, WA 98195-4350, USA
  • GARRY BOWLIN
    Department of Mathematics, Binghamton University, Binghamton, NY 13902, USA
  • THOMAS FLEMING
    Deparment of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, USA
  • JOEL FOISY
    Department of Mathematics, SUNY Potsdam, Potsdam, NY 13676, USA
  • JACOB HENDRICKS
    Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257, USA
  • JASON LACOMBE
    Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, USA

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<jats:p> We show that graphs of the form G <jats:sub>*</jats:sub> K<jats:sub>2</jats:sub> are intrinsically knotted if and only if G is nonplanar. This can be extended to show that G <jats:sub>*</jats:sub> K<jats:sub>5m+1</jats:sub> is intrinsically (m + 2)-linked when G is nonplanar. We also apply this result to classify all complete n-partite graphs with respect to intrinsic knotting and show that this family does not produce any new minor-minimal examples. Finally, we categorize all minor-minimal intrinsically knotted graphs on 8 or fewer vertices. </jats:p>

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