A critical vertex, edge, or set of edges, is one whose deletion lowers the chromatic number.Let $k \geq 4$ and $r \geq 1$ . Must there exist a graph $G$ with chromatic number $k$ such that every vertex is critical, yet every critical set of edges has size $> r$ ?

Worked, still open.

graph theory · open · formalized (Lean) · 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

Yes for **every (k\ge 5)**, and **open for $k=4$**.

llm-hunter · gpt pro 5.2 · unverified

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

AMS 11 · open (literature)

theorem erdos_944 :
    answer(sorry) ↔ ∀ k ≥ 4, ∀ r ≥ 1, ∃ (V : Type u) (G : SimpleGraph V), G.IsErdos944 k r

open