Geodesic
On the $s$-colorful number of a~random hypergraph
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 3, pp. 191-199.

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We study the problem of finding the $s$-colorful number of a random hypergraph in the binomial model. For different probabilities of the edge appearance, we establish asymptotic bounds for the $s$-colorful numbers, which hold with probability tending to $1$. 
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D. A. Shabanov. On the $s$-colorful number of a~random hypergraph. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 3, pp. 191-199. http://geodesic.mathdoc.fr/item/FPM_2018_22_3_a10/

[1] Kupavskii A. B., Shabanov D. A., “Raskraski chastichnykh sistem Shteinera i ikh prilozheniya”, Fundament. i prikl. matem., 18:3 (2013), 77–115

[2] Shabanov D. A., “O suschestvovanii polnotsvetnykh raskrasok dlya ravnomernykh gipergrafov”, Matem. sb., 201:4 (2010), 137–160 | DOI | Zbl

[3] Shabanov D. A., “O kontsentratsii khromaticheskogo chisla sluchainogo gipergrafa”, Dokl. RAN, 475:1 (2017), 24–28 | DOI | Zbl

[4] Alon N., Spencer J., The Probabilistic Method, Wiley, Hoboken, 2016 | MR | Zbl

[5] Dyer M., Frieze A., Greenhill C., “On the chromatic number of a random hypergraph”, J. Combin. Theory, Ser. B, 113 (2015), 68–122 | DOI | MR | Zbl

[6] Janson S., Łuczak T., Rucinski A., Random Graphs, Wiley, New York, 2000 | MR | Zbl

[7] Krivelevich M., Sudakov B., “The chromatic numbers of random hypergraphs”, Random Structures Algorithms, 12:4 (1998), 381–403 | 3.0.CO;2-P class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[8] Schmidt J. P., “Probabilistic analysis of strong hypergraph coloring algorithms and the strong chromatic number”, Discrete Math., 66 (1987), 259–277 | DOI | MR | Zbl

[9] Schmidt-Pruzan J., Shamir E., Upfal E., “Random hypergraph coloring algorithms and the weak chromatic number”, J. Graph Theory, 8 (1985), 347–362 | DOI | MR

[10] Shamir E., “Chromatic numbers of random hypergraphs and associated graph”, Adv. Comput. Research, 5 (1989), 127–142