Abstract
Probably graph coloring concept naturally arose from its application in map coloring: given a map containing several countries, we wish to color the countries in the map in such a way that neighboring countries receive different colors to make the countries distinct. In this chapter we know about vertex coloring, edge coloring, chromatic number, chromatic index, chromatic polynomial, etc.
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References
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Exercises
Exercises
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1.
Obtain vertex coloring of the graphs in Fig. 7.9 with the minimum number of colors.
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2.
Determine the chromatic number of Petersen graph.
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3.
Show that dual graph of a maximal plane graph is a cubic graph.
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4.
Let G be a simple planar graph containing no triangle. Then show that \(\chi (H)\le 4\).
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5.
Show that for a tree of n vertices \(P_G(k)=k(k-1)^{n-1}\).
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6.
Construct a 4-critical graph.
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7.
Let G be a k-critical graph. Then show that the degree of every vertex of G is at least \(k-1\).
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Rahman, M.S. (2017). Graph Coloring. In: Basic Graph Theory. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-49475-3_7
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DOI: https://doi.org/10.1007/978-3-319-49475-3_7
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