8 problems

Let $G$ be a graph, let $t$ be a positive integer, let $\overline{K}_t$ be the edgeless graph on $t$ vertices, and let $G[\overline{K}_t]$ denote the blow-up of $G$ in which each v…

Even inversion blow-up conjecture.

Let $F$ and $F'$ be graphs with chromatic number $r+1$. A graph $H$ is asymptotically weakly $F$-Turán-good if ${\mathrm{ex}}(n,H,F)=(1+o(1))\mathcal N(H,T)$ for some complete $r$-…

Let $H$ be a graph on $m$ edges, let $k$ be a positive integer, let $\delta(H)$ be the minimum degree of $H$, and let $\mathcal{G}_C$ be the graph class defined in the paper. Write…

Let $H$ be a graph with no isolated vertices, let $k$ be a positive integer, and let $\beta(H,k)$ be the optimization parameter defined in the paper. Attainment conjecture for…

Grzesik–Janzer–Nagy conjecture. If

Let $K_{s,t}$ be the complete bipartite graph with $s\leq t$, let $p\geq 3$, and let $\mathcal{M}(K^{p+1}_{s,t})$ denote the matching blow-up family used in the paper. Let…

Blow-up exponent conjecture. For any $0\leq\alpha\leq 1$ and any graph $F$, if