{"schema":"vela.problem-packet.v0.1","problem":628,"statement":"Let $G$ be a graph with chromatic number $k$ containing no $K_k$. If $a,b\\geq 2$ and $a+b=k+1$ then must there exist two disjoint subgraphs of $G$ with chromatic numbers $\\geq a$ and $\\geq b$ respectively?","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)"}