2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66172We 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.16 pages + 6 pages appendixQuantum AlgebraGeometric Topology57M27; 57M25text