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The biclique covering number of a bipartite graph G is the minimum number ofcomplete bipartite subgraphs (bicliques) whose union contains every edge of G.  In this little note we compare three lower bounds on the biclique coveringnumber: A bound jk(G) proposed by Jukna & Kulikov (Discrete Math. 2009); thewell-known fooling set bound fool(G); the "tensor-power" fooling set boundfool^\infty(G). We show jk \le fool le fool^\infty \le min_Q (rk Q)^2, wherethe minimum is taken over all matrices with a certain zero/nonzero-pattern.Only the first inequality is really novel, the third one generalizes a resultof Dietzfelbinger, Hromkovi\v{c}, Schnitger (1994).  We also give examples for which fool \ge (rk)^{log_4 6} improving onDietzfelbinger et al.

On some lower bounds on the number of bicliques needed to cover a bipartite graph