Let $G$ be a finite unit distance graph in ${\mathbb{R}}^2$ (i.e. the vertices are a finite collection of points in ${\mathbb{R}}^2$ and there is an edge between two points if and only if the distance between them is $1$).Is there some $k$ such that if $G$ has girth $\ge k$ (i.e. $G$ contains no cycles of length $<k$) then $\chi (G)\le 3$?

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

This is essentially an old question of Erdős. Wormald already constructed a **4‑chromatic** unit‑distance graph in the plane with **girth 5** (so triangle‑ and 4‑cycle‑free) where the edges are defined **exactly** by unit distances (“join two points whenever their distance is 1”). ([Cambridge University Press & Assessm…

llm-hunter · gpt pro 5.2 · unverified

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