Generalized Turán Number of Even Linear Forests

The generalized Turan number $$ex(n,K_s,H)$$ is defined to be the maximum number of copies of a complete graph $$K_s$$ in any H-free graph on n vertices. Let F be an even linear forest, that is, F consists of paths of even order. In this paper, we determine the value of $$ex(n,K_s,F)$$ , which generalizes or improves some known results on generalized Turan number and classical Turan number.