Induced complete \(h\)-partite graphs in dense clique-less graphs (Q1808156)

Let \(h\), \(a\), and \(b\) be fixed positive integers and \(G\) a graph on \(n\) vertices. It is shown that if \(n\) is sufficiently large, \(\delta(G) \geq (hn)/(n-1)\), and \(G\) contains no \(K_b\), then \(G\) contains at least \((1 - o(1))n/(ha)\) vertex-disjoint induced subgraphs that are complete \(h\)-bipartite graphs \(K(h;a)\) with \(a\) vertices in each of the \(h\) parts. The key result used in the proof is the Alon-Yuster result on the existence of vertex-disjoint \(K(h;a)\)'s.