5 problems

For each integer $k\geq 4$, let $f(k)$ be the auxiliary extremal function from the paper and let $\alpha_{k+2}$ be the coefficient in the asymptotic formula for rainbow saturation,…

Let $K_r$ be the complete graph on $r$ vertices, let $\operatorname{sat}(n,\mathcal{R}(K_r))$ denote the minimum number of edges in an $n$-vertex edge-colored graph containing no r…

Let $C_5$ denote the cycle on five vertices, and let $rsat(n,C_5)$ be its rainbow saturation number. Eventual exact rainbow saturation conjecture for $C_5$. There exists…

Rainbow hypergraph saturation conjecture. For every $k$-uniform hypergraph $H$, we have

Let $K_r$ be the complete graph on $r$ vertices, and let $\operatorname{sat}_{t}\left(n,\mathfrak{R}(K_r)\right)$ denote the minimum number of edges in an $n$-vertex graph whose ed…