If $G$ has infinite chromatic number and is triangle-free (contains no $K_{3}$ ) then must $G$ contain every tree as an induced subgraph?

Worked, still open.

graph theory · open · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

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

Not known in general (for **finite** trees). This is a well‑known open problem of Erdős, attributed to a conjecture of Gyárfás. ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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

open