2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121963We 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.16 pages, 4 figuresGeometric Topology05C10 (Primary) 57M15, 05C35 (Secondary)text