The Burr-Erdős-Graham-Sós conjecture for the seven-cycle

For a graph $H$, let $f(n,e,H)$ be the least number of colors in an edge-coloring of some $n$-vertex graph with at least $e$ edges in which every copy of $H$ is rainbow. Burr, Erdős, Graham, and Sós conjectured that $f(n,\lfloor n^2/4\rfloor+1,C_{2k+1})=(1/8+o(1))n^2$ for every fixed $k\ge3$, and Bu