Generalized short monochromatic odd cycles

Answering a question of Noga Alon, we generalize a result of Janzer and Yip to show that every $k$-edge-coloring of $K_{r^k+1}$ contains a monochromatic subgraph with chromatic number at least $r+1$ and diameter $O(k^{3\mathrm{/}2}{r}^{k\mathrm{/}2}\log r)$.