Intrinsic knotting and linking of almost complete partite graphs

Abstract

We 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. For graphs in these families, we verify a conjecture presented in Adams' "The Knot Book": If a vertex is removed from an intrinsically knotted graph, one obtains an intrinsically linked graph.