SOME RESULTS ON INTRINSICALLY KNOTTED GRAPHS
Paul Blain, Garry Bowlin, Thomas R. Fleming, Joel Foisy, Jacob Hendricks, Jason LaCombe · Journal of Knot Theory and Its Ramifications · 2007
We show that graphs of the form G * K2 are intrinsically knotted if and only if G is nonplanar. This can be extended to show that G * K5m+1 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.