{"schema":"vela.problem-packet.v0.1","problem":561,"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 $G$. Let $F_1$ and $F_2$ be the union of stars. More precisely, let $F_1=\\cup_{i\\leq s} K_{1,n_i}$ and $F_2=\\cup_{j\\leq t} K_{1,m_j}$ with $n_1\\geq \\cdots \\geq n_s\\geq 1$ and $m_1\\geq \\cdots \\geq m_t\\geq 1$. Prove that\\[\\hat{R}(F_1,F_2) = \\sum_{2\\leq k\\leq s+t}l_k\\]where\\[l_k=\\max\\{n_i+m_j-1 : i+j=k\\}.\\]","status":"open","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)"}