Geodesic
Colorings of partial Steiner systems and their applications
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 3, pp. 77-115

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This paper deals with extremal problems concerning colorings of partial Steiner systems. We establish a new sufficient condition for $r$-colorability of a hypergraph from some class of such systems in terms of maximum vertex degree. Moreover, as a corollary we obtain a new lower bound for the threshold probability for $r$-colorability of a random hypergraph in a binomial model. 
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     author = {A. B. Kupavskii and D. A. Shabanov},
     title = {Colorings of partial {Steiner} systems and their applications},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {77--115},
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     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_3_a6/}
}
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A. B. Kupavskii; D. A. Shabanov. Colorings of partial Steiner systems and their applications. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 3, pp. 77-115. http://geodesic.mathdoc.fr/item/FPM_2013_18_3_a6/