%0 Journal Article
%T An extension of Tur¨¢n's Theorem, uniqueness and stability
%A Peter Allen
%A Julia B£¿ttcher
%A Jan Hladky
%A Diana Piguet
%J Mathematics
%D 2014
%I arXiv
%X 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 $M\subset V(G)$. For $(r-1)|M|\ge n$, 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.
%U http://arxiv.org/abs/1403.3801v2