Exact generalized Turán numbers for even linear forests

An even linear forest is a graph whose connected components are all paths of even order. We characterize n-vertex graphs with maximum number of s-cliques and without containing an even linear forest for all values of n. Since a matching is an even linear forest, our result can be viewed as a generalization of the well-known Erdős-Gallai theorem (Erdős and Gallai, 1959 [3]). Moreover, our proof gives a new proof of a result of Wang (2020) [6].