{"schema":"vela.problem-packet.v0.1","problem":720,"statement":"Let $\\hat{R}(G)$ denote the size Ramsey number, the minimal number of edges $m$ such that there is a graph $H$ with $m$ edges such that in any $2$-colouring of the edges of $H$ there is a monochromatic copy of $G$. Is it true that, if $P_n$ is the path of length $n$, then\\[\\hat{R}(P_n)/n\\to \\infty\\]and\\[\\hat{R}(P_n)/n^2 \\to 0?\\]Is it true that, if $C_n$ is the cycle with $n$ edges, then\\[\\hat{R}(C_n) =o(n^2)?\\]","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)"}