Discussiones Mathematicae Graph Theory 15(2) (1995)
185-193
DOI: https://doi.org/10.7151/dmgt.1016
GENERALIZED LIST COLOURINGS OF GRAPHS
Mieczysław Borowiecki Institute of Mathematics |
Peter Mihók Department of Geometry and Algebra |
Abstract
We prove: (1) that chP(G)-χP(G) can be arbitrarily large, where chP(G) and χP(G) are P-choice and P-chromatic numbers, respectively, (2) the (P,L)-colouring version of Brooks' and Gallai's theorems.
Keywords: hereditary property of graphs, list colouring, vertex partition number.
1991 Mathematics Subject Classification: 05C15, 05C70.
References
[1] | M. Borowiecki and P. Mihók, Hereditary Properties of Graphs, in: Advances in Graph Theory (Vishwa International Publications, 1991) 41-68. |
[2] | R.L. Brooks, On colouring the nodes of a network, Proc. Cambridge Phil. Soc. 37 (1941) 194-197, doi: 10.1017/S030500410002168X. |
[3] | P. Erdős, A.L. Rubin and H. Taylor, Choosability in graphs, in: Proc. West Coast Conf. on Combin., Graph Theory and Computing, Congressus Numerantium XXVI (1979) 125-157. |
[4] | T. Gallai, Kritiche Graphen I, Publ. Math. Inst. Hung. Acad. Sci. 8 (1963) 373-395. |
[5] | F. Harary, Graph Theory (Addison Wesley, Reading, Mass. 1969). |
[6] | V.G. Vizing, Colouring the vertices of a graph in prescribed colours (in Russian), Diskret. Analiz 29 (1976) 3-10. |
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