Korándi Dániel Rainbow saturation and graph capacities

The $t$-colored rainbow saturation number $rsat_t(n,F)$ is the minimum size of a $t$-edge-colored graph on $n$ vertices that contains no rainbow copy of $F$, but the addition of any missing edge in any color creates such a rainbow copy. Barrus, Ferrara, Vandenbussche and Wenger conjectured that $rsat_t(n,K_s) = \Theta(n\log n)$ for every $s\ge 3$ and $t\ge$ $\binom{s}{2}$. In this talk I will explain how this problem is related to the Shannon capacity of a certain family of cliques, and use this connection to prove the conjecture in a strong sense, asymptotically determining the rainbow saturation number for triangles.