4 problems

Let $C_{2k}$ be the cycle of length $2k$, and let $\operatorname{ex}^*(n,C_{2k})$ denote the maximum number of edges in a properly edge-colored $n$-vertex graph containing no rainb…

Let $C_{2k}$ denote the cycle of length $2k$, and let $\mathrm{ex}^*(n,H)$ be the maximum number of edges in a properly edge-coloured $n$-vertex graph containing no rainbow copy of…

Halfpap–Anastasia conjecture. This lower bound is best possible. The conjecture has already been proved for $n=3,4$ by Johnston, Palmer, and Sarkar, and for $n=5$ by Halfpap and An…

Connected bipartite rainbow Turán conjecture. If $F$ is bipartite, then ${\mathrm{rb}}(n,F,F)$ and ${\mathrm{ex}}(n,F)$ have the same order of magnitude.