# 19 - 4 5 Determining Chromatic Polynomial By a...

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2 A procedure for coloring small graphs: brute-force assign colors - get upper bound find a subgraph that needs at least that number of colors
3 Theorem. Let G be a planar graph. Then Proof. χ ( G ) 5 . Chromatic Polynomial: Important Note When Counting Colorings Using Chromatic Polynomials: We will assume vertices have unique labels, so two colorings will be considered different if they assign different colors at at least one vertex of the graph G . Chromatic Polynomials for Special Graphs:

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Unformatted text preview: 4 5 Determining Chromatic Polynomial By a Decomposition Method: 6 a and b have the same color in a coloring a and b have different colors in a coloring 7 8 9 Basic Properties of Chromatic Polynomials: 10 11 Fix such a coloring of this 12 13 Let G be a graph and let D be its orientation. Let l ( D ) be the length of a longest (directed) path in D . Then, ( G ) 1 + l ( D ) ....
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## 19 - 4 5 Determining Chromatic Polynomial By a...

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