Given a d-tree d, we say that a pair of nodes, x and y, are related by a d-edge if it is known from d that x dominates y, it is not known from d that x immediately dominates y, and there is no other variable in d that is known to be between them.
a pair of nodes x and y, x ~ y, are related byad-edgeifd ~ x~y,d ~ xGy, and for allz E vars(d),ifd ~ (x&zAz~y) then z = x or z = y.