Feature Column from the AMS

Colorful Mathematics: Part II

5. 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.

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

Fiorini, S. and R. Wilson, Edge-colourings of Graphs, Research Notes in Mathematics, Vol. 16, Pitman, 1977.

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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Hartsfield, N. and G. Ringel, Pearls in Graph Theory, Revised and Augmented Edition, Academic Press, Boston, 1994.

Heesch, H., Zur systematischen Strukturtheorie III, IV, Z. Krist. 73 (1930) 325-345, 346-356.

Heesch, H., Untersuchungen zum Vierfarbenproblem, Mannheim/Wien/Zürich, Biblographisches Institute, 1969.

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Ringel, G. Map Color Theorem, Springer-Verlag, New York, 1974.

Ringel, G., 250 Jahre Graphentheorie, In: Graphen in Forschung und Unterricht: Festschrift K. Wagner, Barbara Franzbecker Verlag, 1985, pp. 136-152.

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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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Robertson, N. and P. Seymour, R. Thomas, Hadwiger's conjecture for K⁶-free graphs, Combinatorica, 13 (1993) 279-361.

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Sanders, D. and Y. Zhao, On simultaneous edge-face colorings of plane graphs, Combinatorica, 17 (1997) 441-445.

Sanders, D. and Y. Zhao, On total 9-coloring planar graphs of maximum degree seven, J. Graph Theory, 31 (1999) 63-73.

Sanders, D. and Y. Zhao, On the entire coloring conjecture, Canad. Math. Bull., 43 (2000) 104-114.

Thomassen, C., Every planar graph is 5-choosable, J. Comb. Theory B, 62 1994) 180-181.

Thomassen, C., Grötzsch's 3-color theorem, J. Comb. Theory B, 62 (1994) 268-279.

Thomassen, C., 3-list coloring planar graphs of girth 5, J. Comb. Theory B, 64 (1995) 101-107.

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Voigt, M. and B. Wirth, On 3-colorable non-4-choosable planar graphs, J. Graph Theory, 24 (1997) 233-235.

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Wagner, K., Ein Satz über Komplexe, Jahresber. Deut. Math. Verein., 46 (Pt. 2) (1936) 21-22.

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.

Wagner, K., Über eine Erweiterung eines Satzes von Kuratowski, Deutsche Math., 2 (1937) 280-280.

Wagner, K., Bermerkungen zu Hadwigers Vermutung, Math. Annalen, 141 (1960) 433-451.

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.

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

Wilson, R., Graphs Colourings and the Four-colour Theorem, Oxford U. Press, 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 these materials.