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 $G$. Determine$$\hat{R}(K_{n,n}),$$where $K_{n,n}$ is the complete bipartite graph with $n$ vertices in each component.

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

This is **not known exactly**: determining the diagonal size–Ramsey number of the balanced complete bipartite graph (K_{n,n}) is an **open problem**. ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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