• Ping Zhang
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


One of the most popular areas of study in graph theory is colorings. This topic can be traced back to the origin of the Four Color Problem and whether it is possible to color the regions of every map with four or fewer colors in such a way that every two regions having a common boundary are assigned different colors. Later it was seen that this problem could be looked at as a problem in graph theory—whether it is always possible to color the regions of every planar graph (embedded in the plane) so that every two adjacent regions are colored differently. It became known that the Four Color Problem could be solved if it could be solved for all bridgeless cubic planar graphs.


  1. 15.
    Brooks, R. L. (1941). On coloring the nodes of a network. Proceedings of the Cambridge Philosophical Society, 37, 194–197.Google Scholar
  2. 19.
    Chartrand, G., & Zhang, P. (2009). Chromatic graph theory. Boca Raton: Chapman & Hall/CRC.zbMATHGoogle Scholar
  3. 22.
    Chartrand, G., Lesniak, L., & Zhang, P. (2010). Graphs & digraphs (5th ed.). Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
  4. 43.
    Fournier, J.-C. (1973). Colorations des arétes d’un graphe. In Colloque sur la Théorie des Graphes (Brussels, 1973) (French). Cahiers Centre Études Recherche Opér (Vol. 15, pp. 311–314).Google Scholar
  5. 69.
    König, D. (1916). Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre. Mathematische Annalen, 77, 453–465MathSciNetCrossRefGoogle Scholar
  6. 76.
    Tait, P. G. (1880). Remarks on the colouring of maps. Proceedings of the Royal Society of Edinburgh, 10, 501–503, 729.zbMATHGoogle Scholar
  7. 78.
    Vizing, V. G. (1964). On an estimate of the chromatic class of a p-graph. Diskret Analiz, 3 (Russian), 25–30.Google Scholar

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© Ping Zhang 2015

Authors and Affiliations

  • Ping Zhang
    • 1
  1. 1.Department of MathematicsWestern Michigan UniversityKalamazooUSA

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