  We classify all the maximal linklessly embeddable graphs of order 12 and show
that their complements are all intrinsically knotted. We derive results about
the connected domination numbers of a graph and its complement. We provide an
answer to an open question about the minimal order of a 3-non-compliant graph.
We prove that the complements of knotlessly embeddable graphs of order at least
15 are all intrinsically knotted. We provide results on general
$k$-non-compliant graphs and leave a set of open questions for further
exploration of the subject.
