Potentially Kr1,r2,...,rl,r,s-graphic sequences

A variation of a classical Turan-type extremal problem is considered as follows: determine the smallest even integer sigma(K,(r1, r2,...,rl,r,s), n) such that every n-term graphic sequence pi = (d(1), d(2),..., d(n)) with term sum sigma(pi) = d(1) + d(2) + (. . .) + d(n) >= sigma(K-r1,K-r2..... rl,K-r,K-s, n) has a realization G containing K-r1,K-r2,K-...,K-rl,K-r,K-s as a subgraph. In this paper, we determine sigma(K-r1,K-r2,K-...,K-rl,K-r,K-s,K- n) for sufficiently large n, where s >= r >= r(l) >= (. . .) > r(1) >= 0 and r >= 3. (c) 2006 Elsevier B.V. All rights reserved.