Let $R_k(G)$ denote the minimal $m$ such that if the edges of $K_m$ are $k$-coloured then there is a monochromatic copy of $G$. Determine$$R_k(K_{s,t})$$where $K_{s,t}$ is the complete bipartite graph with $s$ vertices in one component and $t$ in the other.

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

Because (K_{s,t}\cong K_{t,s}), we may assume (1\le s\le t). In general, $R(K_{s,t};k)$ is **not known exactly**; what is known are sharp results in some special cases and general upper/lower bounds.

llm-hunter · gpt pro 5.2 · unverified

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