{"schema":"vela.problem-packet.v0.1","problem":65,"statement":"Let $G$ be a graph with $n$ vertices and $kn$ edges, and $a_1<a_2<\\cdots $ be the lengths of cycles in $G$. Is it true that\\[\\sum\\frac{1}{a_i}\\gg \\log k?\\]Is the sum $\\sum\\frac{1}{a_i}$ minimised when $G$ is a complete bipartite graph?","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)"}