On the number of 3-edge colorings of cubic graphs
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.
scientific article; zbMATH DE number 1740673