On the number of 3-edge colorings of cubic graphs (Q1348773)
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scientific article; zbMATH DE number 1740673
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of 3-edge colorings of cubic graphs |
scientific article; zbMATH DE number 1740673 |
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On the number of 3-edge colorings of cubic graphs (English)
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23 September 2002
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The Penrose polynomial of a plane cubic graph was introduced by \textit{R. Penrose} [Comb. Math. Appl., Proc. Conf. Math. Inst., Oxford 1969, 221-224 (1971; Zbl 0216.43502)]. In this paper the Penrose polynomial is introduced for binary matroids and it is expressed as a sum of characteristics polynomials of some associated binary matroids. It is presented a short algebraic proof for a generalization of a formula of Penrose on the number of 3-edge colorings of a plane cubic graph and it is shown that the number of 3-edge colorings of cubic graphs can be computed (up to a factor of \(2^{|E|/3-1}\)) by evaluating the Penrose polynomial of their cycle space at 4.
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Penrose polynomial
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plane cubic graph
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3-edge coloring
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binary matroid
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matroids
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