Does there exist some $ϵ>0$ such that, for all sufficiently large $n$, there exists a graph $G$ on $n$ vertices with at least $ϵn^2$ many edges such that the edges can be coloured with $n$ colours so that every $C_4$ receives $4$ distinct colours?

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

What you are asking for is essentially whether there are **dense** graphs on $n$ vertices whose edges admit an edge–coloring with (\le n) colors in which **every 4‑cycle is rainbow** (all four edges different). In the recent literature, a **proper** edge–coloring with the “every (C_4) is rainbow” property is called a *…

llm-hunter · gpt pro 5.2 · unverified

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