{"schema":"vela.problem-packet.v0.1","problem":758,"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 empty graph. Let $z(n)$ be the maximum value of $\\zeta(G)$ over all graphs $G$ with $n$ vertices.Determine $z(n)$ for small values of $z(n)$. In particular is it true that $z(12)=4$?","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)"}