We show that the chromatic number of $G_{n, \frac 12}$ is not concentrated on fewer than $n^{\frac 14 - \varepsilon}$ consecutive values. This addresses a longstanding question raised by Erdős and several other authors.

中文翻译：

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随机图的色数不集中

我们表明 $G_{n, \frac 12}$ 的色数不集中在少于 $n^{\frac 14 - \varepsilon}$ 的连续值上。这解决了 Erdős 和其他几位作者提出的长期问题。