  We give series solutions to single insertion place propagator-type systems of
Dyson--Schwinger equations using binary tubings of rooted trees. These
solutions are combinatorially transparent in the sense that each tubing has a
straightforward contribution. The Dyson--Schwinger equations solved here are
more general than those previously solved by chord diagram techniques,
including systems and non-integer values of the insertion parameter $s$. We
remark on interesting combinatorial connections and properties.
