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2002 | 22 | 1 | 149-158
Tytuł artykułu

Edge colorings and total colorings of integer distance graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An integer distance graph is a graph G(D) with the set Z of integers as vertex set and two vertices u,v ∈ Z are adjacent if and only if |u-v| ∈ D where the distance set D is a subset of the positive integers N. In this note we determine the chromatic index, the choice index, the total chromatic number and the total choice number of all integer distance graphs, and the choice number of special integer distance graphs.
Wydawca
Rocznik
Tom
22
Numer
1
Strony
149-158
Opis fizyczny
Daty
wydano
2002
otrzymano
2000-07-22
poprawiono
2001-01-30
Twórcy
  • Diskrete Mathematik, Technische Universität Braunschweig, Pockelsstr. 14, D-38106 Braunschweig, Germany
  • Diskrete Mathematik, Technische Universität Braunschweig, Pockelsstr. 14, D-38106 Braunschweig, Germany
Bibliografia
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  • [4] G.J. Chang, J.-J. Chen, and K.-Ch. Huang, Integral distance graphs, J. Graph Theory 25 (1997) 287-294, doi: 10.1002/(SICI)1097-0118(199708)25:4<287::AID-JGT6>3.0.CO;2-G
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  • [14] T.R. Jensen and Bjarne Toft, Graph coloring problems (Wiley, New York, 1995).
  • [15] M. Juvan and B. Mohar, List colorings of outerplanar graphs (Manuscript, 1998).
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  • [17] A. Kemnitz and H. Kolberg, Coloring of integer distance graphs, Discrete Math. 191 (1998) 113-123, doi: 10.1016/S0012-365X(98)00099-5.
  • [18] A. Kemnitz and M. Marangio, Chromatic numbers of integer distance graphs, Discrete Math. (to appear).
  • [19] A.V. Kostochka, The total chromatic number of any multigraph with maximum degree five is at most seven, Discrete Math. 162 (1996) 199-214, doi: 10.1016/0012-365X(95)00286-6.
  • [20] D.P. Sanders and Y. Zhao, On total 9-coloring planar graphs of maximum degree seven, J. Graph Theory 31 (1999) 67-73, doi: 10.1002/(SICI)1097-0118(199905)31:1<67::AID-JGT6>3.0.CO;2-C
  • [21] V.G. Vizing, On an estimate of the chromatic class of a p-graph, Metody Diskret. Analiz. 3 (1964) 25-30 (Russian).
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  • [25] X. Zhu, Distance graphs on the real line (Manuscript, 1996).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1164
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