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Chromatic Sums for Rooted Planar Triangulations: The Cases λ = 1 and λ = 2

  • W. T. Tutte (a1)

Summary

In this paper we derive a functional equation whose solution would give the sum of the chromatic polynomial P(M, λ) over certain classes of rooted planar maps M called “ triangulations” and “near-triangulations”. For an integral colour-number λ this sum is the number of λ-coloured rooted maps of the kind considered, but the sum can also be discussed for non-integral λ.

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References

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1. Mullin, R. C., On counting rooted triangular maps, Can. J. Math. 17 (1965), 373382.
2. Tutte, W. T., A census of Hamiltonian polygons, Can. J. Math. 14 (1962), 402417.
3. Tutte, W. T., A contribution to the theory of chromatic polynomials, Can. J. Math. 6 (1953), 8091.
4. Tutte, W. T., Connectivity in graphs (University of Toronto Press, Toronto, 1966).
5. Tutte, W. T., On chromatic polynomials and the golden ratio, J. Combinatorial Theory 9 (1970), 289296.
6. Tutte, W. T., On the enumeration of four-colored maps, SIAM J. Appl. Math. 17 (1969), 454460.
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Chromatic Sums for Rooted Planar Triangulations: The Cases λ = 1 and λ = 2

  • W. T. Tutte (a1)

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