Advertisement

Chromatic sums revisited

Chapter
  • 90 Downloads

Summary

This paper discusses some equations arising in the author’s work on “chromatic sums”. The main results were presented in a series of papers extending from 1973 to 1982. The object here is to give a unified and simplified account of the elimination of unwanted variables from the initial equation, leading to the final identification of the desired chromatic sums as the coefficients in a power series satisfying a certain differential equation.

Keywords

Power Series Constant Term Polynomial Identity Chromatic Polynomial Special Invariant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Beraha, S., Private communication.Google Scholar
  2. [2]
    Tutte, W. T., A census of planar triangulations,Canad. J. Math. 16 (1962),21–38.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Tutte, W. T., Chromatic sums for rooted planar triangulations; the cases λ = 1 and λ = 2. Canad. J. Math. 25 (1973), 426–447.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Tutte, W. T., Chromatic sums for rooted planar triangulations II: the case λ = τ + 1. Canad. J. Math. 25 (1973), 657–671.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Tutte, W. T., Chromatic sums for rooted planar triangulations III; the case.i = 3. Canad. J. Math. 25 (1973),780–790.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Tutte, W. T., Chromatic sums for rooted planar triangulations IV; the case λ = ⋡. Canad. J. Math. 25 (1973),929–940.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Tutte, W. T., Chromatic sums for rooted planar triangulations V; special equations. Canad. J. Math.26 (1974),893–907.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Tutte, W. T., On a pair of functional equations of combinatorial interest. Aequationes Math. 17 (1978), 121–140.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    Tutte, W. T., Chromatic solutions. Canad. J. Math. 34 (1982), 741–758.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    Tutte, W. T., Chromatic solutions II. Canad. J. Math. 34 (1982), 952–960.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Tutte, W. T., The matrix of chromatic joins. J. Combin. Theory Ser. B 57 (1993),269–288.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel 1995

Authors and Affiliations

  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

Personalised recommendations