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4 hours ago comment added mathworker21 You should really write ${X \choose 2}$ instead of $[X]^2$. Anyways, the chromatic number of $G(n,\frac{1}{2})$ is very concentrated around $\frac{\log 2}{2}\frac{n}{\log n}$, so much so that $\bigl(1+o(1)\bigr)\frac{\log 2}{2}\frac{n}{\log n}$ is its mean. So the answer to your question is $0$. (Look up "Erdos-Renyi" graph).
20 hours ago history asked Dominic van der Zypen CC BY-SA 4.0