We determine the maximum number of edges of an n-vertex graph G with the
property that none of its r-cliques intersects a fixed set M⊂V(G).
For (r−1)∣M∣≥n, the (r−1)-partite Turan graph turns out to be the unique
extremal graph. For (r−1)∣M∣<n, there is a whole family of extremal graphs,
which we describe explicitly. In addition we provide corresponding stability
results.Comment: 12 pages, 1 figure; outline of the proof added and other referee's
comments incorporate