Graph partition into small cliques

Let s and k be two integers with 0 ? s ? k and let G be a simple graph of order n . This paper investigates clique partition problems. It is proved that if n ? 3 s + 4 ( k - s ) and d ( u ) + d ( v ) ? 3 ( n - s ) / 2 + k - 1 for any pair of non-adjacent vertices u , v of G , then G contains s vertex-disjoint K 3 s and k - s vertex-disjoint K 4 s such that all of them are vertex-disjoint. Moreover, the degree condition is sharp.