{"schema":"vela.problem-packet.v0.1","problem":753,"statement":"The list chromatic number $\\chi_L(G)$ is defined to be the minimal $k$ such that for any assignment of a list of $k$ colours to each vertex of $G$ (perhaps different lists for different vertices) a colouring of each vertex by a colour on its list can be chosen such that adjacent vertices receive distinct colours.Does there exist some constant $c>0$ such that\\[\\chi_L(G)+\\chi_L(G^c)> n^{1/2+c}\\]for every graph $G$ on $n$ vertices (where $G^c$ is the complement of $G$)?","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)"}