On two limit values of the chromatic number of a~random hypergraph
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 2, pp. 223-246
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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 $p$.
Keywords:
random hypergraph, chromatic number, second moment method.
@article{TVP_2022_67_2_a1,
author = {Yu. A. Demidovich and D. A. Shabanov},
title = {On two limit values of the chromatic number of a~random hypergraph},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {223--246},
publisher = {mathdoc},
volume = {67},
number = {2},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_2_a1/}
}
TY - JOUR AU - Yu. A. Demidovich AU - D. A. Shabanov TI - On two limit values of the chromatic number of a~random hypergraph JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2022 SP - 223 EP - 246 VL - 67 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2022_67_2_a1/ LA - ru ID - TVP_2022_67_2_a1 ER -
Yu. A. Demidovich; D. A. Shabanov. On two limit values of the chromatic number of a~random hypergraph. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 2, pp. 223-246. http://geodesic.mathdoc.fr/item/TVP_2022_67_2_a1/