{"schema":"vela.problem-packet.v0.1","problem":80,"statement":"Let $c>0$ and let $f_c(n)$ be the maximal $m$ such that every graph $G$ with $n$ vertices and at least $cn^2$ edges, where each edge is contained in at least one triangle, must contain a book of size $m$, that is, an edge shared by at least $m$ different triangles. Estimate $f_c(n)$. In particular, is it true that $f_c(n)>n^{\\epsilon}$ for some $\\epsilon>0$? Or $f_c(n)\\gg \\log n$?","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)"}