{"schema":"vela.problem-packet.v0.1","problem":1016,"statement":"Let $h(n)$ be minimal such that there is a graph on $n$ vertices with $n+h(n)$ edges which contains a cycle on $k$ vertices, for all $3\\leq k\\leq n$. Estimate $h(n)$. In particular, is it true that\\[h(n) \\geq \\log_2n+\\log_*n-O(1),\\]where $\\log_*n$ is the iterated logarithmic function?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A105206","name":"Number of edges in a pancyclic graph on n+2 vertices with the fewest possible edges.","terms":"3,5,6,8,9,10,12,13,14,15,16,17,19,20,21,22,23,24,25,26","url":"https://oeis.org/A105206"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}