Theory of Probability &Its Applications, Volume 67, Issue 2, Page 175-193, August 2022.
The limit concentration of the values of the chromatic number of the random hypergraph $H(n,k,p)$ in the binomial model is studied. It is proved that, for a fixed $k\ge 3$ and with not too rapidly increasing $n^{k-1}p$, the chromatic number of the hypergraph $H(n,k,p)$ lies, with probability tending to 1, in the set of two consecutive values. Moreover, it is shown that, under slightly stronger constraints on the growth of $n^{k-1}p$, these values can be explicitly evaluated as functions of $n$ and $p$.

中文翻译：

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一个随机超图的色数的两个极限值

概率论及其应用，第 67 卷，第 2 期，第 175-193 页，2022 年 8 月
。研究了二项式模型中随机超图 $H(n,k,p)$ 的色数值的极限浓度. 证明了，对于一个固定的$k\ge 3$ 并且$n^{k-1}p$ 增长不是太快，超图$H(n,k,p)$ 的色数位于，有在两个连续值的集合中，概率趋于 1。此外，它表明，在对 $n^{k-1}p$ 增长的稍强约束下，这些值可以明确地评估为 $n$ 和 $p$ 的函数。