{"schema":"vela.problem-packet.v0.1","problem":803,"statement":"We call a graph $H$ $D$-balanced (or $D$-almost-regular) if the maximum degree of $H$ is at most $D$ times the minimum degree of $H$.Is it true that for every $m\\geq 1$, if $n$ is sufficiently large, any graph on $n$ vertices with $\\geq n\\log n$ edges contains a $O(1)$-balanced subgraph with $m$ vertices and $\\gg m\\log m$ edges (where the implied constants are absolute)?","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)"}