Geodesic
Chromatic Solutions
Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 741-758

Voir la notice de l'article provenant de la source Cambridge University Press

Early in the Seventies I sought the number of rooted λ-coloured triangulations of the sphere with 2p faces. In these triangulations double joins, but not loops, were permitted. The investigation soon took the form of a discussion of a certain formal power series l(y, z, λ) in two independent variables y and z.The basic theory of l is set out in [1]. There l is defined as the coefficient of x 2 in a more complicated power series g(x, y, z, λ). But the definition is equivalent to the following formula. 1 Here T denotes a general rooted triangulation. n(T) is the valency of its root-vertex, and 2p(T) is the number of its faces. P(T, λ) is the chromatic polynomial of the graph of T. 
Tutte, W. T. Chromatic Solutions. Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 741-758. doi: 10.4153/CJM-1982-051-4
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[1] 1. Tutte, W. T., Chromatic sums for rooted planar triangulations: the cases λ = 1 and λ = 2, Can. J. Math. 25 (1973), 426–447. Google Scholar

[2] 2. Tutte, W. T., Chromatic sums for rooted planar triangulations II: the case λ = ⸆ +• l, Can. J. Math. 25 (1973), 657–671. Google Scholar

[3] 3. Tutte, W. T., Chromatic sums for rooted planar triangulations III: the case λ = 3, Can. J. Math. 25 (1973), 780–790. Google Scholar

[4] 4. Tutte, W. T., Chromatic sums for rooted planar triangulations V: special equations, Can. J. Math. 26 (1974), 893–907. Google Scholar

[5] 5. Tutte, W. T., On a pair of functional equations of combinatorial interest, Aequationes Math. 17 (1978), 121–140. Google Scholar

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