Let be a simple graph, and for every list assignment let be the maximum number of vertices of which are colorable with respect to . Define , where the minimum is taken over all list assignments with for all .

**Conjecture**[2] Let be a graph with list chromatic number and . Then

As you see this conjecture in the special case , is the conjecture of Albertson, Grossman and Haas [1]: for any .

## Bibliography

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

[2] Moharram N. Iradmusa, A Note on Partial List Colorings, *Australasian Journal of Combinatorics*, Vol.46, 2010, .

* indicates original appearance(s) of problem.