Skip to main content Accessibility help
×
Home

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

  • W. T. Tutte (a1)

Summary

The chromial P(M, λ) of a planar near-triangulation M has the leading term λ v(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 MS, that is we get the number of members of S.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

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

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Copyright

References

Hide All
1. Mullin, R. C., On counting rooted triangular maps, Can. J. Math. 17 (1965), 373382.
2. Read, R. C., An introduction to chromatic polynomials,]. Combinatorial Theory 4 (1968), 5271.
3. Tutte, W. T., A census of Hamiltonian polygons, Can. J. Math. U (1962), 402-417.
4. Tutte, W. T., On chromatic polynomials and the golden ratio, J. Combinatorial Theory 9 (1970), 289296.
5. Tutte, W. T., Chromatic sums for rooted planar triangulations, I, II, and III, Can. J. Math. 25 (1973), 426447; 657-671; 780-790.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

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

  • W. T. Tutte (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed