Colorful Mathematics: Part IV

Feature Column Archive

6. References

Appel, K. and W. Haken, Every Planar Map is Four Colorable, American Mathematical Society, Providence, 1989.

Bodendiek, R. (ed.), Graphen in Forschung und Unterricht, Festschrift K. Wagner, Dad Salzdetfurth: Barbara Franzbecker.

Bogart, K., Discrete Mathematics, Heath, Lexington, MA., 1988.

Borodin, O., On cyclic coloring of planar graphs, Discrete Math., 100 (1992) 281-289.

Borodin, O., Cyclic degree and cyclic colorings of 3-polytopes, J. of Graph Theory, 23 (1996) 225-231.

Borodin, O., Structural theorem on plane graphs with application to the entire coloring number, J. of Graph Theory, 23 (1996) 233-239.

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Cozzens, M. and F. Roberts, T-colorings of graphs and the channel assignment problem, Congr. Numer. 35 (1982) 191-208.

Cozzens, M. and D.-I. Wang, The general channel assignment problem, Congr. Numer. 41 (1984) 115-129.

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Dirac, G., Percy John Heawood, J. London Math. Soc., 38 (1963) 263-277.

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Fritsch, R. and G. Fritsch, The Four-Color Theorem, Springer-Verlag, New York, 1998.

Grünbaum, B., Convex Polytopes, Wiley-Interscience, New York, 1967. (Second edition, 2003.)

Gutner, S., The complexity of planar graph choosability, Discrete Math., 159 (1996) 119-130.

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Robertson, N., and D. Sanders, P. Seymour, R. Thomas, Every 2-connected cubic graph with no Petersen minor is 3-edge colorable. (To appear.)

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Tesman, B., set T-colorings, Congr. Numer. 77 (1990) 229-242.

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Wagner, K., Zwei Bermerkungen über Komplexe, Math. Annalen, 112 (1936) 316-321.

Wagner, K., Über eine Eigenschaft der ebenen Komplexe, Math. Annalen, 114 (1937) 570-590.

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Wagner, K. Beweis eine Abschwächung der Hadwiger-Vermutung, Math. Annalen, 153 (1964) 139-141.

Waller, Simultaneously colouring the edges and faces of plane graphs, J. Combin. Theory B, 69 (1997) 219-221.

Wang, D.-I., The channel assignment problem and closed neighborhood containment graphs, Ph.D. Thesis, Northeastern U., Boston, MA., 1985.

West, D., Introduction to Graph Theory, Second Edition, Prentice-Hall, Upper Saddle River, 2001.

Wilson, R., Graphs Colourings and the Four-colour Theorem, Oxford, Oxford, 2002.

Those who can access JSTOR can find some of the papers mentioned above there. For those with access, the American Mathematical Society's MathSciNet can be used to get additional bibliographic information and reviews of some of these materials.

  1. Introduction
  2. Resolving conflicts (I)
  3. Resolving conficts (II)
  4. From schoolgirls to tournaments
  5. Mathematics and cell phones
  6. References