3 problems

All graphs considered are finite and simple. For a graph $G$, write $\rho(G)$ for its chromatic number and $\tau(G)$ for its clique number. A graph is minimally nonperfectly divisi…

A graph $H$ is weakly $K_k$-Turán-good when, for all sufficiently large $n$, some complete $(k-1)$-partite graph attains ${\mathrm{ex}}(n,H,K_k)$. An edge of a graph $F$ is color-c…

Let $G$ be a graph, let $\chi(G)$ denote its chromatic number, and let $K_t$ be the complete graph on $t$ vertices. An $H$-immersion is an injective mapping of $V(H)$ to $V(G)$ tog…