{"schema":"vela.problem-packet.v0.1","problem":667,"statement":"Let $p,q\\geq 1$ be fixed integers. We define $H(n)=H(N;p,q)$ to be the largest $m$ such that any graph on $n$ vertices where every set of $p$ vertices spans at least $q$ edges must contain a complete graph on $m$ vertices.Is\\[c(p,q)=\\liminf \\frac{\\log H(n)}{\\log n}\\]a strictly increasing function of $q$ for $1\\leq q\\leq \\binom{p-1}{2}+1$?","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)"}