On the choosability of complete multipartite graphs with part size three (Q1969804)

Let \(K_{m*r}\) be the complete \(r\)-partite graph with \(m\) vertices in each part. \textit{P. Erdős, A. L. Rubin} and \textit{H. Taylor} [Combinatorics, graph theory and computing, Proc. West Coast Conf., Arcata/Calif. 1979, 125-157 (1980; Zbl 0469.05032)] showed that \(K_{2*r}\) is \(r\)-choosable and suggested the problem of determining the choosability of \(K_{m*r}\). The author of the present paper proves that \(K_{3*r}\) is exactly \(\lceil(4r-1)/3 \rceil\)-choosable.