We say that a graph is $4$ -chromatic critical if it has chromatic number $4$ , and removing any edge decreases the chromatic number to $3$ .Is there, for arbitrarily large $n$ , a $4$ -chromatic critical graph on $n$ vertices with minimum degree $≫ n$ ?

Worked, still open.

graph theory · open · possible · 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

As far as the literature currently records, this is **open**.

llm-hunter · gpt pro 5.2 · unverified

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

open