Discussiones Mathematicae Graph Theory 17(1) (1997)
127-132
DOI: https://doi.org/10.7151/dmgt.1045
ON GENERALIZED LIST COLOURINGS OF GRAPHS
Mieczysław Borowiecki Institute of Mathematics |
Izak Broere Department of Mathematics |
Peter Mihók Mathematical Institute of Slovak Academy of Sciences |
Abstract
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.
Keywords: hereditary property of graphs, list colouring, vertex partition number.
1991 Mathematics Subject Classification: 05C15, 05C70.
References
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