  A graph H is strongly immersed in G if H is obtained from G by a sequence of
vertex splittings (i.e., lifting some pairs of incident edges and removing the
vertex) and edge removals. Equivalently, vertices of H are mapped to distinct
vertices of G (branch vertices) and edges of H are mapped to pairwise
edge-disjoint paths in G, each of them joining the branch vertices
corresponding to the ends of the edge and not containing any other branch
vertices. We describe the structure of graphs avoiding a fixed graph as a
strong immersion.
