4 problems

Let $s<n/4$, and let $H$ be an $n$-vertex graph with $\operatorname{ex}_n(K_3)+s$ edges, where $\operatorname{ex}_n(K_3)$ is the maximum number of edges in an $n$-vertex triangle-f…

Let $\alpha,\beta,\gamma\in[0,1]$, let $R_2\subseteq[0,1]^3$ be the second region defined in the paper, and let $H_9$ be the specified tripartite graph. For a weighting $w$,…

Let $\alpha,\beta,\gamma\in[0,1]$ be edge densities of a weighted tripartite graph, let $R\subseteq[0,1]^3$ be the region defined in the paper, let $R_2=R\setminus R_1$, and let…

Let $\alpha,\beta,\gamma\in[0,1]$ be the prescribed edge densities, let $T_{\min}(\alpha,\beta,\gamma)$ denote the minimum triangle density over weighted tripartite graphs with the…