Abstract
This paper shows that with B = { 1 , 2 , … , n } , the smallest k such that ( B × B ) − { ( j , j ) | j ∈ B } = ⋃ i = 1 k ( C i × D i ) is s ( n ) , where s ( n ) is the smallest integer k such that n ⩽ ( k ⌊ k 2 ⌋ ) . This provides a simple set-based formulation and a new proof of a result for boolean ranks (de Caen et al., 1981 [2]) and biclique covering of bipartite graphs (Berukov et al., 2008 [1]; Fronček et al., 2007 [5]), making these intricate results more accessible.
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