Abstract
A biclique is a maximal induced complete bipartite subgraph. The biclique graph of a graph H , denoted by K B ( H ) , is the intersection graph of the family of all bicliques of H . In this work we address the following question: Given a biclique graph G = K B ( H ) , is it possible to remove a vertex q of G , such that G − { q } is a biclique graph? And if possible, can we obtain a graph H ′ such that G − { q } = K B ( H ′ ) ? We show that the general question has a “no” for answer. However, we prove that if G has a vertex q such that d ( q ) = 2 , then G − { q } is a biclique graph and we show how to obtain H ′ .
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