**Conjecture**Let be a simple graph with vertices and list chromatic number . Suppose that and each vertex of is assigned a list of colors. Then at least vertices of can be colored from these lists.

Albertson, Grossman, and Haas introduce this interesting question in [AGH], and prove some partial results. For instance, they show that under the above assumptions, at least vertices of can be colored from the lists.

## Bibliography

*[AGH] M. Albertson, S. Grossman and R. Haas, Partial list colouring, Discrete Math., **214**(2000), pp. 235-240.

* indicates original appearance(s) of problem.