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A \emph{biclique} is a maximal bipartite complete induced subgraph of $G$.Bicliques have been studied in the last years motivated by the large number ofapplications. In particular, enumeration of the maximal bicliques has been ofinterest in data analysis. Associated with this issue, bounds on the maximumnumber of bicliques were given. In this paper we study bounds on the minimunnumber of bicliques of a graph. Since adding false-twin vertices to $G$ doesnot change the number of bicliques, we restrict to false-twin-free graphs. Wegive a tight lower bound on the minimum number bicliques for a subclass of$\{C_4$,false-twin$\}$-free graphs and for the class of$\{K_3$,false-twin$\}$-free graphs. Finally we discuss the problem for generalgraphs.

Tight lower bounds on the number of bicliques in false-twin-free graphs