Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-15T10:53:54.245Z Has data issue: false hasContentIssue false
  • English
  • Français

Chromatic Sums for Rooted Planar Triangulations, IV: The Case λ = ∞

Published online by Cambridge University Press:  20 November 2018

W. T. Tutte
W. T. Tutte*
Affiliation:
University of Waterloo, Waterloo, Ontario
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The chromial P(M, λ) of a planar near-triangulation M has the leading term λv(M), where v(M) is the number of vertices of M. The problem of finding the number of rooted planar near-triangulations of a given class S, all supposed to have the same number of vertices, can be regarded as a special case of the problem of finding chromatic sums. We can sum P(M, λ) over the members of S, divide by the appropriate power of λ and let λ → ∞. We thus get the sum of the coefficient of the leading term of P(M, λ) for all M ∈ S, that is we get the number of members of S.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 929 - 940
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Mullin, R. C., On counting rooted triangular maps, Can. J. Math. 17 (1965), 373–382.Google Scholar
2. Read, R. C., An introduction to chromatic polynomials,]. Combinatorial Theory 4 (1968), 52–71.Google Scholar
3. Tutte, W. T., A census of Hamiltonian polygons, Can. J. Math. U (1962), 402-417.Google Scholar
4. Tutte, W. T., On chromatic polynomials and the golden ratio, J. Combinatorial Theory 9 (1970), 289–296.Google Scholar
5. Tutte, W. T., Chromatic sums for rooted planar triangulations, I, II, and III, Can. J. Math. 25 (1973), 426–447; 657-671; 780-790.Google Scholar