Abstract

The asymptotic behavior of the chromatic number of the binomial random hypergraph \(H(n,k,p)\) is studied in the case when \(k \geqslant 4\) is fixed, n tends to infinity, and p = p(n) is a function. If p = p(n) does not decrease too slowly, we prove that the chromatic number of \(H(n,k,p)\) is concentrated in two or three consecutive values, which can be found explicitly as functions of n, p, and k.

中文翻译：

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关于随机超图的色数

摘要

研究在固定\（k \ geqslant 4 \），n趋于无穷且p = p的情况下，二项式随机超图\（H（n，k，p）\）的色数的渐近行为。（n）是一个函数。如果p = p（n）的下降不是太慢，我们证明\（H（n，k，p）\）的色数集中在两个或三个连续的值中，这些值可以明确地作为n的函数找到，p和k。