{"schema":"vela.problem-packet.v0.1","problem":759,"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 $z(S_n)$ be the maximum value of $\\zeta(G)$ over all graphs $G$ which can be embedded on $S_n$, the orientable surface of genus $n$. Determine the growth rate of $z(S_n)$.","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)"}