{"schema":"vela.problem-packet.v0.1","problem":86,"statement":"Let $Q_n$ be the $n$-dimensional hypercube graph (so that $Q_n$ has $2^n$ vertices and $n2^{n-1}$ edges). Is it true that every subgraph of $Q_n$ with\\[\\geq \\left(\\frac{1}{2}+o(1)\\right)n2^{n-1}\\]many edges contains a $C_4$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A245762","name":"Maximal number of edges in a C_4 free subgraph of the n-cube.","terms":"1,3,9,24,56,132","url":"https://oeis.org/A245762"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}