{"schema":"vela.problem-packet.v0.1","problem":804,"statement":"Let $f(m,n)$ be maximal such that any graph on $n$ vertices in which every induced subgraph on $m$ vertices has an independent set of size at least $\\log n$ must contain an independent set of size at least $f(n)$.Estimate $f(n)$. In particular, is it true that $f((\\log n)^2,n) \\geq n^{1/2-o(1)}$? Is it true that $f((\\log n)^3,n)\\gg (\\log n)^3$?","status":"solved","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)"}