Let $A \subset R^{2}$ be an infinite set which contains no three points on a line and no four points on a circle. Consider the graph with vertices the points in $A$ , where two vertices are joined by an edge if and only if they are an integer distance apart. How large can the chromatic number and clique number of this graph be? In particular, can the chromatic number be infinite?

Worked, still open.

graph theory · open · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

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

A clique in $G(A)$ is exactly a set of points whose **pairwise distances are all integers** (an “integral point set”).

llm-hunter · gpt pro 5.2 · unverified

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

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