Abstract
The biclique graphKB(G) is the intersection graph of all the bicliques of a graph G. The aim of our work is to recognize graphs that are biclique graphs of interval bigraphs (IBG). In this paper we prove that KB(IBG)⊂K1,4-free co-comparability graphs. We also study the class of biclique graphs of proper interval bigraphs (PIB). Recall that PIB is equal to the class of bipartite permutation graphs (BPG). We present a characterization of the class KB(PIB) and of the biclique graphs of a subclass of PIB that leads to a polynomial time recognition algorithm. We also present characterizations of biclique graphs of some classes such as complete graphs, trees and graphs with girth at least 5.
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