On vertex-induced weighted Turán problems (Q2237208)

In this paper, the authors consider the vertex-induced weighted Turán problems introduced by \textit{P. Bennett} et al. [ibid. 342, No. 8, 2165--2172 (2019; Zbl 1418.05079)], being mainly focused on the sum-edge-weight Turán problems. They first characterize the extremal structure of \(K_{\ell}\)-free graph under sum-edge-weight function and give the similarities and differences with the previous structure under product-edge-weight function. Based on the results of complete graphs, a generalized version of the Erdős-Stone theorem for weighted graphs was proposed under both of the two types of vertex-induced weight functions.