{"schema":"vela.problem-packet.v0.1","problem":920,"statement":"Let $f_k(n)$ be the maximum possible chromatic number of a graph with $n$ vertices which contains no $K_k$.Is it true that, for $k\\geq 4$,\\[f_k(n) \\gg \\frac{n^{1-\\frac{1}{k-1}}}{(\\log n)^{c_k}}\\]for some constant $c_k>0$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}