Abstract
The generalized Turán number ex(n,Ks,H) is the maximum number of complete graph Ks in an H-free graph on n vertices. Let Fk be the friendship graph consisting of k triangles. Erdős and Sós (1976) determined the value of ex(n,K3,F2). Alon and Shikhelman (2016) proved that ex(n,K3,Fk)≤(9k−15)(k+1)n. In this paper, by using a method developed by Chung and Frankl in hypergraph theory, we determine the exact value of ex(n,K3,Fk) and the extremal graph for any Fk when n≥4k3.
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