Geodesic
Chromatic Sums for Rooted Planar Triangulations, III: The Case λ = 3
Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 780-790

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

In this paper we are chiefly concerned with the chromatic sums we have called l and h, with colour-number 3. In this case h can be interpreted as enumerating the rooted Eulerian triangulations with a given number of faces, and l as enumerating such triangulations with a given number of faces and a given valency for the root-vertex. The series h has been determined already, by summation from the formula enumerating even slicings [3]. However our formula for l does not seem to have been published before, though it could presumably be derived in a similar way. 
Tutte, W. T. Chromatic Sums for Rooted Planar Triangulations, III: The Case λ = 3. Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 780-790. doi: 10.4153/CJM-1973-080-7
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[1] 1. Birkhoff, G. D. and Lewis, D. C., Chromatic polynomials, Trans. Amer. Math. Soc. 60 (1946), 355–451. Google Scholar

[2] 2. Tutte, W. T., A census of planar maps, Can. J. Math. 15 (1963), 249–271. Google Scholar

[3] 3. Tutte, W. T. A census of slicings, Can. J. Math. U (1962), 708-722. Google Scholar

[4] 4. Tutte, W. T. Chromatic sums for rooted planar triangulations: the cases X = 1 and X = 2, Can. J. Math. 25 (1973), 426–447. Google Scholar

[5] 5. Tutte, W. T. Chromatic sums for rooted planer triangulations, II: the case X = r -f- 1, Can. J. Math. 25 (1973), 657–671. Google Scholar

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