{"schema":"vela.problem-packet.v0.1","problem":613,"statement":"Let $n\\geq 3$ and $G$ be a graph with $\\binom{2n+1}{2}-\\binom{n}{2}-1$ edges. Must $G$ be the union of a bipartite graph and a graph with maximum degree less than $n$?","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)"}