Intrinsic knotting and linking of almost complete graphs
J. Campbell, T. W. Mattman, R. Ottman, J. Pyzer, M. Rodrigues, S. Williams
Abstract
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.
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