A connected graph G is called a pseudo-tree if its vertex-set V(G) admits a partition π into finite classes such that the derived graph G/π (having the classes of π as its vertices) is a tree; if in addition π can be chosen in such a way that each class of π induces a connected subgraph of G, then G is called a quasi-tree. For instance, all connected locally finite graphs are quasi-trees. We characterize the pseudo-trees by forbidden configurations and investigate the structure of pseudo-trees which are not quasi-trees.
