erdős #165
Give an asymptotic formula for .
Worked, still open.
graph theory · open · prize $250 · 0 attempts
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unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
Let (R(3,k)) be the least (n) such that every red/blue colouring of (E(K_n)) contains either a red triangle or a blue (K_k) (equivalently: every triangle‑free graph on (n) vertices has an independent set of size (k)). ([arXiv][1])
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗oeis
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#544Show thatas . Similarly, prove or disprove thatA000791#553Let denote the smallest integer such that if we -colour the edges of then there is either a monochromatic triangle in one of the first two colours or a monochromatic in the third colour. Define similarly but with two colours. Show thatas .A000791#986For any fixed ,for some constant .A000791#1030Let be the usual Ramsey number: the smallest such that if the edges of are coloured red and blue then there exists either a red or a blue .Prove the existence of some such thatA000791status
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