  We examine spaces of connected tri-/univalent graphs subject to local
relations which are motivated by the theory of Vassiliev invariants. It is
shown that the behaviour of ladder-like subgraphs is strongly related to the
parity of the number of rungs: there are similar relations for ladders of even
and odd lengths, respectively. Moreover, we prove that - under certain
conditions - an even number of rungs may be transferred from one ladder to
another.
