{"schema":"vela.problem-packet.v0.1","problem":1013,"statement":"Let $h_3(k)$ be the minimal $n$ such that there exists a triangle-free graph on $n$ vertices with chromatic number $k$. Find an asymptotic for $h_3(k)$, and also prove\\[\\lim_{k\\to \\infty}\\frac{h_3(k+1)}{h_3(k)}=1.\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A292528","name":"Minimal number of vertices in a triangle-free graph with chromatic number n.","terms":"1,2,5,11,22","url":"https://oeis.org/A292528"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}