Ge–Xu–Zhang conjecture for clique odd-colourings

For a graph $H$, let $r_H(n)$ be the least number of colours in an edge-colouring of $K_n$ with no even-chromatic copy of $H$. For a clique $K_t$, having an even number of edges is equivalent to $t\equiv 0,1\pmod 4$.

Ge–Xu–Zhang conjecture. For every positive integer $t\geq 4$ with $t\equiv 0,1\pmod 4$,

$$r_{K_t}(n)=n^{o(1)}.$$

For these values of $t$, $K_t$ is not even-decomposable, so this is the clique case predicted by Versteegen's conjecture. The cases $t=4$ and $t=5$ are established in the paper, while the general statement remains open.