Have a personal or library account? Click to login
Enumeration of rooted 3-connected bipartite planar maps Cover

Enumeration of rooted 3-connected bipartite planar maps

Open Access
|Jun 2022

References

  1. [1] O. Bernardi and M. Bousquet-Mélou, Counting colored planar maps: algebraicity results, J. Combin. Theory Ser. B, 101 (2011) 315–377.10.1016/j.jctb.2011.02.003
  2. [2] M. Bousquet-Mélou, Counting planar maps, coloured or uncoloured, In: Chapman, R. (Ed.), Surveys in Combinatorics 2011 (London Mathematical Society Lecture Note Series), Cambridge: Cambridge University Press, pp. 1–50.10.1017/CBO9781139004114.002
  3. [3] M. Drmota, Random Trees. An Interplay between Combinatorics and Probability, Springer-Verlag Wien, 2009.10.1007/978-3-211-75357-6
  4. [4] F. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge: Cambridge University Press, 2009.10.1017/CBO9780511801655
  5. [5] V. A. Liskovets and T. R. S. Walsh, Enumeration of eulerian and unicursal planar maps, Discrete Math., 282 (2004) 209–221.10.1016/j.disc.2003.09.015
  6. [6] R. Mullin, B. L. Richmond and R. G. Stanton, An asymptotic relation for bicubic maps, Congr. Numer., 9 (1974) 345–355.
  7. [7] M. Noy, C. Requilé and J. Rué, Enumeration of labelled 4-regular planar graphs, Proc. Lond. Math. Soc. (3), 119 (2019) 358–378.10.1112/plms.12234
  8. [8] M. Noy, C. Requilé and J. Rué, Further results on random cubic planar graphs, Random Structures & Algorithms 56(3) (2020) 892–924.10.1002/rsa.20893
  9. [9] M. Noy, C. Requilé and J. Rué, Asymptotic enumeration of labelled 4-regular planar graphs, arXiv:2001.05943.
  10. [10] W. T. Tutte, A census of planar triangulations, Canad. J. Math., 14 (1962) 21–38.10.4153/CJM-1962-002-9
  11. [11] W. T. Tutte, A census of planar maps, Canad. J. Math., 15 (1963) 249–271.10.4153/CJM-1963-029-x
  12. [12] W. T. Tutte, Dichromatic sums for rooted planar maps, Proc. Sympos. Pure Math., 19 (1971) 235–245.10.1090/pspum/019/0319809
  13. [13] W. T. Tutte, Chromatic sums for rooted planar triangulations: the cases λ = 1 and λ = 2, Canad. J. Math., 25 (1973) 426–447.10.4153/CJM-1973-043-3
Language: English
Page range: 97 - 105
Submitted on: Mar 31, 2022
Accepted on: May 15, 2022
Published on: Jun 18, 2022
Published by: Corvinus University of Budapest
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2022 Marc Noy, Clément Requilé, Juanjo Rué, published by Corvinus University of Budapest
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.