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 .
As you see this conjecture in the special case , is the conjecture of Albertson, Grossman and Haas : for any .
 M. Albertson, S. Grossman and R. Haas, Partial list colouring, Discrete Math., 214(2000), pp. 235-240.
 Moharram N. Iradmusa, A Note on Partial List Colorings, Australasian Journal of Combinatorics, Vol.46, 2010, .
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