Choice numbers, Ohba numbers and Hall numbers of some complete k-partite graphs

Abstract

The choice numbers of some complete k−partite graphs are found, after we resolved a dispute regarding the choice number of K(4, 2, . . . , 2) when k is odd. Estimates of the choice numbers and the Ohba numbers of K(m, n, 1, . . . , 1) and K(m, n, 2, . . . , 2) are also discussed for various values of n and m. Finally we close this research with the Hall numbers of K(m, 2, . . . , 2) when m = 2,4.