On biclique coverings

It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bipartite graph Kn,nKn,n with a perfect matching removed can be covered by k   bicliques, then n⩽k⌊k2⌋. We give a slightly simplified proof and we show that the result is tight. Moreover, we use the result to prove analogous bounds for coverings of some other classes of graphs by bicliques.