Turán Number of the Family Consisting of a Blow-up of a Cycle and a Blow-up of a Star.

Let be a family of graphs. The Turán number of the family ℱ is the maximum number of edges in an n-vertex {H1, ..., Hk}-free graph, denoted by ex(n, ℱ ) or ex(n, {H1,H2, ... Hk}). The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different. In this paper we determine the Turán number of the family consisting of a blow-up of a cycle and a blow-up of a star in terms of the Turán number of the family consisting of a cycle, a star and linear forests with k edges. [ABSTRACT FROM AUTHOR]