  We say that a graph is intrinsically knotted or completely 3-linked if every
embedding of the graph into the 3-sphere contains a nontrivial knot or a
3-component link any of whose 2-component sublink is nonsplittable. We show
that a graph obtained from the complete graph on seven vertices by a finite
sequence of $\triangle Y$-exchanges and $Y \triangle$-exchanges is a
minor-minimal intrinsically knotted or completely 3-linked graph.
