The threshold for random k-SAT is 2k (ln 2 - O(k))
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Colouring powers of cycles from random lists
European Journal of Combinatorics
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Random $k$-SAT: Two Moments Suffice to Cross a Sharp Threshold
SIAM Journal on Computing
Coloring graphs from random lists of size 2
European Journal of Combinatorics
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Let Kn,n be the complete bipartite graph with n vertices in each side. For each vertex draw uniformly at random a list of size k from a base set S of size s = s(n). In this paper we estimate the asymptotic probability of the existence of a proper coloring from the random lists for all fixed values of k and growing n. We show that this property exhibits a sharp threshold for k ≥ 2 and the location of the threshold is precisely s(n) = 2n for k = 2 and approximately $s(n)={{n}\over{2^{k-1}\ln 2}}$ for k ≥ 3. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006