{"schema":"vela.problem-packet.v0.1","problem":626,"statement":"Let $k\\geq 4$ and $g_k(n)$ denote the largest $m$ such that there is a graph on $n$ vertices with chromatic number $k$ and girth $>m$ (i.e. contains no cycle of length $\\leq m$). Does\\[\\lim_{n\\to \\infty}\\frac{g_k(n)}{\\log n}\\]exist?Conversely, if $h^{(m)}(n)$ is the maximal chromatic number of a graph on $n$ vertices with girth $>m$ then does\\[\\lim_{n\\to \\infty}\\frac{\\log h^{(m)}(n)}{\\log n}\\]exist, and what is its value?","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)"}