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 (𝓟,k)-choosability have been proved. In this paper we prove some extensions of the well-known bounds for the 𝓟-chromatic number to the (𝓟,k)-choice number and then an extension of Brooks' theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1045,
author = {Mieczys\l aw Borowiecki and Izak Broere and Peter Mih\'ok},
title = {On generalized list colourings of graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {17},
year = {1997},
pages = {127-132},
zbl = {0903.05022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1045}
}
Mieczysław Borowiecki; Izak Broere; Peter Mihók. On generalized list colourings of graphs. Discussiones Mathematicae Graph Theory, Tome 17 (1997) pp. 127-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1045/
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