Erdős Problem 561

### What is the conjecture

https://www.erdosproblems.com/561

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 $F_2=\cup_{j\leq t} K_{1,m_j}$. Prove that
$$\hat{R}(F_1,F_2) = \sum_{2\leq k\leq s+2}\max\\{n_i+m_j-1 : i+j=k\\}.$$

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

The issue provides the Erdős Problems 561 link and states the size Ramsey number conjecture to formalize and prove. Start by reviewing the repository's existing formalized conjectures and Lean setup; done means the stated equality is represented and proved in Lean.

Written by the indexing model from the issue text.