Let $f(n,k)$ be such that every graph on $n$ vertices and $k$ edges can be partitioned into at most $f(n,k)$ edge-disjoint complete graphs. Estimate $f(n,k)$ for $k>n^2/4$.

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

Write (\operatorname{cp}(G)) for the **clique partition number** of $G$: the minimum $t$ such that $E(G)$ can be partitioned into $t$ edge-disjoint complete graphs. Then [ f(n,k)=\max{\operatorname{cp}(G): |V(G)|=n,\ |E(G)|=k}. ]

llm-hunter · gpt pro 5.2 · unverified

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