# List coloring of complete multipartite graphs

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 1, page 31-37
- ISSN: 2083-5892

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topTomáš Vetrík. "List coloring of complete multipartite graphs." Discussiones Mathematicae Graph Theory 32.1 (2012): 31-37. <http://eudml.org/doc/270922>.

@article{TomášVetrík2012,

abstract = {The choice number of a graph G is the smallest integer k such that for every assignment of a list L(v) of k colors to each vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from L(v). We present upper and lower bounds on the choice number of complete multipartite graphs with partite classes of equal sizes and complete r-partite graphs with r-1 partite classes of order two.},

author = {Tomáš Vetrík},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {list coloring; choice number; complete multipartite graph},

language = {eng},

number = {1},

pages = {31-37},

title = {List coloring of complete multipartite graphs},

url = {http://eudml.org/doc/270922},

volume = {32},

year = {2012},

}

TY - JOUR

AU - Tomáš Vetrík

TI - List coloring of complete multipartite graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2012

VL - 32

IS - 1

SP - 31

EP - 37

AB - The choice number of a graph G is the smallest integer k such that for every assignment of a list L(v) of k colors to each vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from L(v). We present upper and lower bounds on the choice number of complete multipartite graphs with partite classes of equal sizes and complete r-partite graphs with r-1 partite classes of order two.

LA - eng

KW - list coloring; choice number; complete multipartite graph

UR - http://eudml.org/doc/270922

ER -

## References

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- [5] H.A. Kierstead, On the choosability of complete multipartite graphs with part size three, Discrete Math. 211 (2000) 255-259, doi: 10.1016/S0012-365X(99)00157-0. Zbl0944.05031
- [6] Zs. Tuza, Graph colorings with local constraints -- a survey, Discuss. Math. Graph Theory 17 (1997) 161-228, doi: 10.7151/dmgt.1049. Zbl0923.05027
- [7] V.G. Vizing, Coloring the vertices of a graph in prescribed colors, Diskret. Analiz 29 (1976) 3-10 (in Russian).
- [8] D.R. Woodall, List colourings of graphs, in: Surveys in Combinatorics, London Mathematical Society Lecture Note Series 288 (Cambridge University Press, 2001) 269-301. Zbl0979.05047
- [9] D. Yang, Extension of the game coloring number and some results on the choosability of complete multipartite graphs, PhD Thesis, (Arizona State University 2003).

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