On generalized list colourings of graphs

• Autorzy: Mieczysław Borowiecki , Izak Broere , Peter Mihók
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hereditary property of graphs; list colouring; vertex partition number

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C70: Factorization, matching, partitioning, covering and packing

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1997
• Tom: 17
• Numer: 1
• Strony: 127-132

Daty

wydano

1997

otrzymano

1997-01-25

Twórcy

autor

Mieczysław Borowiecki

• Institute of Mathematics, Technical University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

autor

Izak Broere

• Department of Mathematics, Rand Afrikaans University, P.O. Box 524, Auckland Park, 2006 South Africa

autor

Peter Mihók

• Mathematical Institute of Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovakia

Bibliografia

• [1] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discussiones Mathematicae Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
• [2] M. Borowiecki and P. Mihók, Hereditary Properties of Graphs, in: Advances in Graph Theory (Vishwa International Publications, 1991) 41-68.
• [3] M. Borowiecki, E. Drgas-Burchardt, Generalized list colourings of graphs, Discussiones Math. Graph Theory 15 (1995) 185-193, doi: 10.7151/dmgt.1016.
• [4] R.L. Brooks, On colouring the nodes of a network, Proc. Cambridge Phil. Soc. 37 (1941) 194-197, doi: 10.1017/S030500410002168X.
• [5] G. Chartrand and H.H. Kronk, The point arboricity of planar graphs, J. London Math. Soc. 44 (1969) 612-616, doi: 10.1112/jlms/s1-44.1.612.
• [6] G. Chartrand and L. Lesniak, Graphs and Digraphs, Second Edition, (Wadsworth & Brooks/Cole, Monterey, 1986).
• [7] G. Dirac, A property of 4-chromatic graphs and remarks on critical graphs, J. London Math. Soc. 27 (1952) 85-92, doi: 10.1112/jlms/s1-27.1.85.
• [8] 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.
• [9] T. Gallai, Kritiche Graphen I, Publ. Math. Inst. Hung. Acad. Sci. 8 (1963) 373-395.
• [10] T.R. Jensen and B. Toft, Graph Colouring Problems, (Wiley-Interscience Publications, New York, 1995).
• [11] A.V. Kostochka, M. Stiebitz and B. Wirth, The colour theorems of Brooks and Gallai extended, Discrete Math. 162 (1996) 299-303, doi: 10.1016/0012-365X(95)00294-7.
• [12] P. Mihók, An extension of Brooks' theorem, in: Proc. Fourth Czechoslovak Symp. on Combin., Combinatorics, Graphs, Complexity (Prague, 1991) 235-236.
• [13] S.K. Stein, B-sets and planar graphs, Pacific J. Math. 37 (1971) 217-224.
• [14] C. Thomassen, Color-critical graphs on a fixed surface (Report, Technical University of Denmark, Lyngby, 1995).
• [15] V.G. Vizing, Colouring the vertices of a graph in prescribed colours, Diskret. Analiz 29 (1976) 3-10 (in Russian).

Identyfikatory

DOI

10.7151/dmgt.1045