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2012 | 32 | 1 | 31-37
Tytuł artykułu

List coloring of complete multipartite graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
32
Numer
1
Strony
31-37
Opis fizyczny
Daty
wydano
2012
otrzymano
2009-01-26
poprawiono
2011-01-11
zaakceptowano
2011-01-11
Twórcy
  • School of Mathematical Sciences, University of KwaZulu-Natal, Durban, South Africa
Bibliografia
  • [1] N. Alon, Choice numbers of graphs; a probabilistic approach, Combinatorics, Probability and Computing 1 (1992) 107-114, doi: 10.1017/S0963548300000122.
  • [2] H. Enomoto, K. Ohba, K. Ota and J. Sakamoto, Choice number of some complete multi-partite graphs, Discrete Math. 244 (2002) 55-66, doi: 10.1016/S0012-365X(01)00059-0.
  • [3] P. Erdös, A.L. Rubin and H. Taylor, Choosability in graphs, in: Proceedings of the West-Coast Conference on Combinatorics, Graph Theory and Computing, Arcata, California (Congr. Numer. XXVI, 1979) 125-157.
  • [4] S. Gravier and F. Maffray, Graphs whose choice number is equal to their chromatic number, J. Graph Theory 27 (1998) 87-97, doi: 10.1002/(SICI)1097-0118(199802)27:2<87::AID-JGT4>3.0.CO;2-B
  • [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.
  • [6] Zs. Tuza, Graph colorings with local constraints -- a survey, Discuss. Math. Graph Theory 17 (1997) 161-228, doi: 10.7151/dmgt.1049.
  • [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.
  • [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).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1583
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