On a generalization of Rubin's theorem

The work is devoted to the calculation of asymptotic value of the choice number of the complete r-partite graph Km* r = Km, …, m with equal part size m. We obtained the asymptotics in the case lnr = o(lnm). The proof generalizes the classical result of A.L. Rubin for the case r = 2. © 2010 Wiley Periodicals, Inc. J Graph Theory 67: 226–234, 2011 67: 226-234, 2011 © 2011 Wiley Periodicals, Inc.