  In some cases, an important example being at finite temperature, extreme
infrared, collinear, or light-cone behaviour may cause the usual loop expansion
to break down. For some of these cases higher order ladder graphs can become
important. In an earlier paper it was shown that, given a particular relation
between a vertex and a self-energy function, the resummation of the ladder
graphs simplifies significantly when other types of graphs are included in a
consistent effective expansion. In this paper we show that this assumed
relation is valid for a large class of vertex and self-energy functions at
finite temperature.
