Biclique graph of bipartite permutation graphs

The biclique graph KB(G) is the intersection graph of bicliques of a graph G. The aim of our work is to recognize graphs that are biclique graphs of bipartite permutation graphs. In this paper we prove that the biclique graph of a bipartite permutation graph is a K1,4-free interval graph, and we present a characterization of such graphs and a characterization of a subclass that leads to a polynomial time recognition algorithm.