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Introduction

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A Kaleidoscopic View of Graph Colorings

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

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Abstract

One of the major areas within graph theory is that of colorings, namely region colorings of graphs embedded on surfaces, vertex colorings and edge colorings. Of all these colorings, the most studied and most popular graph colorings are the vertex colorings. These colorings came about through coloring the regions of planar graphs, that is, through coloring the regions of maps. In this chapter, we review some fundamental concepts and results on vertex and edge colorings that will be encountered as we proceed. In addition, we review some facts concerning degrees of vertices in graphs, outdegrees and indegrees of vertices in digraphs as well as Eulerian graphs and digraphs. Finally, a fundamental fact from discrete mathematics is mentioned that will be encountered often. We refer to the book [15] for graph theory notation and terminology not described here.

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References

  1. Brooks, R.L.: On coloring the nodes of a network. Proc. Camb. Philol. Soc. 37, 194–197 (1941)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chartrand, G., Zhang, P.: Chromatic Graph Theory. Chapman & Hall/CRC Press, Boca Raton (2009)

    MATH  Google Scholar 

  3. Chvátal, V.: Some relations among invariants of graphs. Czech. Math. J. 21, 366–368 (1971)

    MathSciNet  MATH  Google Scholar 

  4. Euler, L.: Solutio problematis ad geometriam situs pertinentis. Comment. Academiae Sci. I. Petropolitanae 8, 128–140 (1736)

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  5. König, D.: Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre. Math. Ann. 77, 453–465 (1916)

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  6. Vizing, V.G.: On an estimate of the chromatic class of a p-graph (Russian). Diskret. Analiz. 3, 25–30 (1964)

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  7. Wilson, R.: Four Colors Suffice: How the Map Problem Was Solved. Princeton University Press, Princeton, NJ (2002)

    MATH  Google Scholar 

  8. Zhang, P.: Color-Induced Graph Colorings. Springer, New York (2015)

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Western Michigan University, Kalamazoo, MI, USA

    Ping Zhang

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  1. Ping Zhang
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Zhang, P. (2016). Introduction. In: A Kaleidoscopic View of Graph Colorings. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-30518-9_1

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