  We give a complete characterization of bipartite graphs having tree-like
Galois lattices. We prove that the poset obtained by deleting bottom and top
elements from the Galois lattice of a bipartite graph is tree-like if and only
if the graph is a Bipartite Distance Hereditary graph. By relying on the
interplay between bipartite distance hereditary graphs and series-parallel
graphs, we show that the lattice can be realized as the containment relation
among directed paths in an arborescence. Moreover, a compact encoding of
Bipartite Distance Hereditary graphs is proposed, that allows optimal time
computation of neighborhood intersections and maximal bicliques.
