Generalized Turan numbers for the edge blow-up of a graph

Let H be a graph and p be an integer. The edge blow-up Hp of H is the graph obtained from replacing each edge in H by a copy of Kp where the new vertices of the cliques are all distinct. Let Ck and Pk denote the cycle and path with k vertices, respectively. In this paper, we find sharp upper bounds for ex(n, K3, C33) and the exact value for ex(n, K3, P43). Moreover, we determine the graphs attaining these bounds.(c) 2023 Elsevier B.V. All rights reserved.