{"schema":"vela.problem-packet.v0.1","problem":807,"statement":"The bipartition number $\\tau(G)$ of a graph $G$ is the smallest number of pairwise edge disjoint complete bipartite graphs whose union is $G$. The independence number $\\alpha(G)$ is the size of the largest independent subset of $G$.Is it true that, if $G$ is a random graph on $n$ vertices with edge probability $1/2$, then\\[\\tau(G)=n-\\alpha(G)\\]almost surely?","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)"}