Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-11-20 , DOI: 10.1016/j.disc.2020.112231 Arseniy E. Balobanov; Dmitry A. Shabanov
This paper deals with estimating the threshold for the strong -colorability of a random 3-uniform hypergraph in the binomial model . A vertex coloring is said to be strong for a hypergraph if every two vertices sharing a common edge are colored with distinct colors. It is known that the threshold corresponds to the sparse case, when the expected number of edges is a linear function of , , and depends on , but not on . We establish the threshold as a bound on the parameter up to an additive constant. In particular, by using the second moment method we prove that for large enough and , the random hypergraph is strongly -colorable with high probability and, vice versa, for , it is not strongly -colorable with high probability.