Graphic sequences with a realization containing a complete multipartite subgraph

A nonincreasing sequence of nonnegative integers @p=(d"1,d"2,...,d"n) is graphic if there is a (simple) graph G of order n having degree sequence @p. In this case, G is said to realize@p. For a given graph H, a graphic sequence @p is potentiallyH-graphic if there is some realization of @p containing H as a (weak) subgraph. Let @s(@p) denote the sum of the terms of @p. For a graph H and n@?Z^+, @s(H,n) is defined as the smallest even integer m so that every n-term graphic sequence @p with @s(@p)>=m is potentially H-graphic. Let K"s^t denote the complete t partite graph such that each partite set has exactly s vertices. We show that @s(K"s^t,n)=@s(K"("t"-"2")"s+K"s","s,n) and obtain the exact value of @s(K"j+K"s","s,n) for n sufficiently large. Consequently, we obtain the exact value of @s(K"s^t,n) for n sufficiently large.