{"schema":"vela.problem-packet.v0.1","problem":744,"statement":"Let $k$ be a large fixed constant. Let $f_k(n)$ be the minimal $m$ such that there exists a graph $G$ on $n$ vertices with chromatic number $k$, such that every proper subgraph has chromatic number $<k$, and $G$ can be made bipartite by deleting $m$ edges. Is it true that $f_k(n)\\to \\infty$ as $n\\to \\infty$? In particular, is it true that $f_4(n) \\gg \\log n$?","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)"}