{"schema":"vela.problem-packet.v0.1","problem":1077,"statement":"We call a graph $D$-balanced (or $D$-almost-regular) if the maximum degree is at most $D$ times the minimum degree.Let $\\epsilon,\\alpha>0$ and $D$ and $n$ be sufficiently large. If $G$ is a graph on $n$ vertices with at least $n^{1+\\alpha}$ edges, then must $G$ contain a $D$-balanced subgraph on $m>n^{1-\\alpha}$ vertices with at least $\\epsilon m^{1+\\alpha}$ edges?","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)"}