Extremal graphs for clique-paths
  In this paper we deal with a Tur\'an-type problem: given a positive integer n and a forbidden graph H, how many edges can there be in a graph on n vertices without a subgraph H? How does a graph look like if it has this extremal edge number?   The forbidden graph in this article is a clique-path: a path of length k where each edge is extended to an r-clique, r >2. We determine both the extremal number and the extremal graphs for sufficiently large n. 
Roman Glebov
math.CO