Multigraphs without large bonds are wqo by contraction
  We show that the class of multigraphs with at most $p$ connected components and bonds of size at most $k$ is well-quasi-ordered by edge contraction for all positive integers $p,k$. (A bond is a minimal non-empty edge cut.) We also characterize canonical antichains for this relation and show that they are fundamental. 
Marcin Kami\'nski, Jean-Florent Raymond, Th\'eophile Trunck
math.CO