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Chromatic sums of biloopless nonseparable near-triangulations on the projective plane

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Abstract

In this paper, the chromatic sum functions of rooted biloopless nonseparable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived.

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References

  1. Bender, E.A. Asymptotic methods in enumeration. SIAM Rev., 16: 485–515 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  2. Gao, Z.C. The number of rooted 2-connected triangular maps on the projective plane. J. Combin. Theory B, 53: 130–142 (1991)

    Article  MATH  Google Scholar 

  3. Liu Yanpei. Enumerative Theory of Maps. Kluwer, Dordrecht, Boston, London, 1999

    MATH  Google Scholar 

  4. Liu Yanpei. On chromatic and dichromatic sum equations for planar maps. Discrete Math., 84: 167–179 (1990)

    Article  Google Scholar 

  5. Liu Yanpei. Chromatic sum equations for rooted nonseparable planar maps. Comm. Appl. Math. Comput., 2: 1–11 (1988) (in Chinese)

    MathSciNet  Google Scholar 

  6. Tutte W T. Chromatic sums for rooted planar triangulations: the case λ = 1 and λ = 2. Canad. J. Math., 25: 426–447 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  7. Tutte W T. Chromatic sums for rooted planar triangulations II: the case λ = τ +1. Canad. J. Math., 25: 657–671 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  8. Tutte W T. Chromatic sums for rooted planar triangulations III: the case λ = 3. Canad. J. Math., 25: 780–790 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  9. Tutte W T. Chromatic sums for rooted planar triangulations IV: the case λ = ∞. Canad. J. Math., 26: 309–325 (1974)

    Article  MathSciNet  Google Scholar 

  10. Tutte W T. Chromatic sums for rooted planar triangulations V: special function. Canad. J. Math., 26: 893–907 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tutte W T. A census of planar triangulations. Canad. J. Math., 14: 21–38 (1962)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Minzu University of China, Beijing, 100081, China

    Zhao-xiang Li

  2. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Yan-pei Liu

  3. School of Traffic and Transportation, Beijing Jiaotong University, Beijing, 100044, China

    Bing-feng Si

Authors
  1. Zhao-xiang Li
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  2. Yan-pei Liu
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  3. Bing-feng Si
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Corresponding author

Correspondence to Zhao-xiang Li.

Additional information

Supported by the National Natural Science Foundation of China (No. 10771225; 10871021; 71071016) and Fundamental Research Funds for the Central Universities.

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Li, Zx., Liu, Yp. & Si, Bf. Chromatic sums of biloopless nonseparable near-triangulations on the projective plane. Acta Math. Appl. Sin. Engl. Ser. 29, 123–134 (2013). https://doi.org/10.1007/s10255-013-0197-3

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  • DOI: https://doi.org/10.1007/s10255-013-0197-3

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