A note on partial list coloring

Albertson, Grossman and Haas in [Discrete Math. 214 (2000), 235-240] conjecture that if L is a t-list assignment for a graph G and 1 <= t <= chi(l) (G), then at least (sic) vertices of G can be colored from these lists where chi(l) (G) is the list chromatic number of G. In this note we investigate the partial list coloring conjecture. Precisely, we show that the conjecture is true for at least half of the numbers in the set {1, 2,..., chi(l) (G) - 1}. In addition, we introduce a new related conjecture and finally we present some results about this conjecture.