{"schema":"vela.problem-packet.v0.1","problem":917,"statement":"Let $k\\geq 4$ and $f_k(n)$ be the largest number of edges in a graph on $n$ vertices which has chromatic number $k$ and is critical (i.e. deleting any edge reduces the chromatic number).Is it true that\\[f_k(n) \\gg_k n^2?\\]Is it true that\\[f_6(n)\\sim n^2/4?\\]More generally, is it true that, for $k\\geq 6$,\\[f_k(n) \\sim \\frac{1}{2}\\left(1-\\frac{1}{\\lfloor k/3\\rfloor}\\right)n^2?\\]","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)"}