Fast recognition of classes of almost-median graphs

In this paper it is shown that a class of almost-median graphs that includes all planar almost-median graphs can be recognized in O(m log n) time, where n denotes the number of vertices and m the number of edges. Moreover, planar almost-median graphs can be recognized in linear time. As a key auxiliary result we prove that all bipartite outerplanar graphs are isometric subgraphs of the hypercube and that the embedding can be effected in linear time.