{"schema":"vela.problem-packet.v0.1","problem":610,"statement":"For a graph $G$ let $\\tau(G)$ denote the minimal number of vertices that include at least one from each maximal clique of $G$ (aside from isolated vertices). This is sometimes called the clique transversal number.Estimate $\\tau(G)$. In particular, is it true that if $G$ has $n$ vertices then\\[\\tau(G) \\leq n-\\omega(n)\\sqrt{n}\\]for some $\\omega(n)\\to \\infty$, or even\\[\\tau(G) \\leq n-c\\sqrt{n\\log n}\\]for some absolute constant $c>0$?","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)"}