8 problems

Let integers $\ell\geq r\geq 3$, and let ${\mathcal T}_r(n,\ell)$ denote the complete balanced $\ell$-partite $r$-uniform hypergraph. Write $K_{\ell+1}^r$ for the complete $r$-unif…

Let $K_{\ell+1}^{(r)+}$ be the $r$-uniform expansion of the complete graph on $\ell+1$ vertices, let $M_{s+1}^{(r)+}$ be an $r$-uniform matching with $s+1$ edges, and let…

Let ${\mathrm{ex}}^{\sum}_r(n,k,K_\ell^{(r)+})$ denote the rainbow hyper-Turán number for the $r$-uniform expansion $K_\ell^{(r)+}$, and let $t_r(n,\ell-1)$ be the number of edges…

Let $K^{(r)+}_{\ell+1}$ be the $r$-uniform expansion of the complete graph on $\ell+1$ vertices, let $M^{(r)+}_{s+1}$ be an $r$-uniform matching with $s+1$ edges, and let…

Let $G$ be a graph with chromatic number $\chi(G)=\ell>r$, and let $U$ be an independent set of $G$ such that deleting $U$ results in a graph $G_0$ of chromatic number $\ell-1$. Su…

Let $\mathcal{T}_r(n,\ell)$ be the complete balanced $\ell$-partite $r$-graph, and let $K^{(r)+}_{\ell+1}$ be the $r$-uniform expansion of the complete graph on $\ell+1$ vertices.…

Let $K^{(r)+}_3$ denote the $r$-uniform expansion of the triangle, and let ${\mathrm{ex}}_r(n,K^{(r)+}_3)$ be its $r$-uniform Turán number. Erdős's expanded-triangle conjecture. Fo…

Given an integer $r\geq 3$, let $K_3^r$ be the $r$-uniform expansion of the complete graph $K_3$, and let ${\rm ex}_r(n,K_3^r)$ denote the maximum number of edges in an $r$-uniform…