A note on bipartite graph tiling

Bipartite graph tiling was studied by Zhao [SIAM J. Discrete Math., 23 (2009), pp. 888-900], who gave the best possible minimum degree conditions for a balanced bipartite graph on 2ms vertices to contain m vertex disjoint copies of K _s, _s. Let s < t be fixed positive integers. Hladký and Schacht [SIAM J. Discrete Math., 24 (2010), pp. 357-362] gave minimum degree conditions for a balanced bipartite graph on 2m(s + t) vertices to contain m vertex disjoint copies of K _s, _t. Their results were best possible, except in the case when m is odd and t > 2s+1. We give the best possible minimum degree condition in this case.