  For a degree sequence, we define the set of edges that appear in every
labeled realization of that sequence as forced, while the edges that appear in
none as forbidden. We examine structure of graphs whose degree sequences
contain either forced or forbidden edges. Among the things we show, we
determine the structure of the forced or forbidden edge sets, the relationship
between the sizes of forced and forbidden sets for a sequence, and the
resulting structural consequences to their realizations. This includes showing
that the diameter of every realization of a degree sequence containing forced
or forbidden edges is no greater than 3, and that these graphs are maximally
edge-connected.
