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Chromatic Sums for Rooted Planar Triangulations, III: The Case λ = 3

Published online by Cambridge University Press:  20 November 2018

W. T. Tutte
W. T. Tutte*
Affiliation:
University of Waterloo, Waterloo, Ontario
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Summary

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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 780 - 790
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Birkhoff, G. D. and Lewis, D. C., Chromatic polynomials, Trans. Amer. Math. Soc. 60 (1946), 355–451.Google Scholar
2. Tutte, W. T., A census of planar maps, Can. J. Math. 15 (1963), 249–271.Google Scholar
3. Tutte, W. T. A census of slicings, Can. J. Math. U (1962), 708-722.Google Scholar
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. 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