  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.
