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. In particular, 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. 1 

• Type: Journal
• Year: 2007
• Where: DM
• Authors: Wilfried Imrich, Alenka Lipovec, Iztok Peterin, Petra Zigert
• Keywords: Almost-median Graphs, Bipartite Outerplanar Graphs, DM 2007, Linear Time