DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory  17(1) (1997)   127-132
DOI: 10.7151/dmgt.1045

ON GENERALIZED LIST COLOURINGS OF GRAPHS

Mieczysław Borowiecki

Institute of Mathematics
Technical University of Zielona Góra
Podgórna 50, 65-246 Zielona Góra, Poland
e-mail: m.borowiecki@im.uz.zgora.pl

Izak Broere

Department of Mathematics
Rand Afrikaans University
P.O. Box 524, Auckland Park, 2006 South Africa
e-mail: ib@rau3.rau.ac.za

Peter Mihók

Mathematical Institute of Slovak Academy of Sciences
Grešákova 6, 040 01 Košice, Slovakia
e-mail: mihok@Košice.upjs.sk

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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