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 $F_1={\cup }_{i\le s}{K}_{1,n_i}$ and $F_2={\cup }_{j\le t}{K}_{1,m_j}$ with $n_1\ge \cdots \ge n_s\ge 1$ and $m_1\ge \cdots \ge m_t\ge 1$. Prove that$$\hat{R}(F_1,F_2)=\sum _{2\le k\le s+t}{l}_k$$where$$l_k=\max \{n_i+m_j-1:i+j=k\}.$$

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

First, a small indexing remark: for [ F_1=\bigcup_{i=1}^s K_{1,n_i}\qquad\text{and}\qquad F_2=\bigcup_{j=1}^t K_{1,m_j}, ] the natural symmetric formula has the sum running to $s+t$: [ \boxed{\ \hat R(F_1,F_2)\stackrel{?}= \sum_{k=2}^{s+t}\max{,n_i+m_j-1:\ i+j=k,}\ }. ] [[nomath]](Your upper limit $s+2$ is exactly the …

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.