{"schema":"vela.problem-packet.v0.1","problem":760,"statement":"The cochromatic number of $G$, denoted by $\\zeta(G)$, is the minimum number of colours needed to colour the vertices of $G$ such that each colour class induces either a complete graph or independent set. If $G$ is a graph with chromatic number $\\chi(G)=m$ then must $G$ contain a subgraph $H$ with\\[\\zeta(H) \\gg \\frac{m}{\\log m}?\\]","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)"}