{"schema":"vela.problem-packet.v0.1","problem":75,"statement":"Is there a graph of chromatic number $\\aleph_1$ with $\\aleph_1$ vertices such that for all $\\epsilon>0$ if $n$ is sufficiently large and $H$ is a subgraph on $n$ vertices then $H$ contains an independent set of size $>n^{1-\\epsilon}$? What about an independent set of size $\\gg n$?","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)"}