Geodesic
On generalized list colourings of graphs
Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 1, pp. 127-132

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Vizing [15] and Erdős et al. [8] independently introduce the idea of considering list-colouring and k-choosability. In the both papers the choosability version of Brooks' theorem [4] was proved but the choosability version of Gallai's theorem [9] was proved independently by Thomassen [14] and by Kostochka et al. [11]. In [3] some extensions of these two basic theorems to (,k)-choosability have been proved.
Keywords: hereditary property of graphs, list colouring, vertex partition number 
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Borowiecki, Mieczysław; Broere, Izak; Mihók, Peter. On generalized list colourings of graphs. Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 1, pp. 127-132. http://geodesic.mathdoc.fr/item/DMGT_1997_17_1_a8/