INTRINSIC LINKING IN DIRECTED GRAPHS

We extend the notion of intrinsic linking to directed graphs. We give methods of constructing intrinsically linked directed graphs, as well as complicated directed graphs that are not intrinsically linked. We prove that the double directed version of a graph G is intrinsically linked if and only if G is intrinsically linked. One Corollary is that J6, the complete symmetric directed graph on 6 vertices (with 30 directed edges), is intrinsically linked. We further extend this to show that it is possible to find a subgraph of J6 by deleting 6 edges that is still intrinsically linked, but that no subgraph of J6 obtained by deleting 7 edges is intrinsically linked. We also show that J6 with an arbitrary edge deleted is intrinsically linked, but if the wrong two edges are chosen, J6 with two edges deleted can be embedded linklessly.