Intrinsic knotting and linking of almost complete graphs

J. Campbell, T. W. Mattman, R. Ottman, J. Pyzer, M. Rodrigues, S. Williams

Published 2007-01-15Version 1

We introduce new sufficient conditions for intrinsic knotting and linking. A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted. We also classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respect to intrinsic linking and intrinsic knotting. In addition, we classify intrinsic knotting of graphs on 8 vertices.