Geodesic
The distribution of the number of small cuts in a random planar triangulation
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010) Cet article a éte moissonné depuis la source Episciences

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We enumerate rooted 3-connected (2-connected) planar triangulations with respect to the vertices and 3-cuts (2-cuts). Consequently, we show that the distribution of the number of 3-cuts in a random rooted 3-connected planar triangulation with $n+3$ vertices is asymptotically normal with mean $(10/27)n$ and variance $(320/729)n$, and the distribution of the number of 2-cuts in a random 2-connected planar triangulation with $n+2$ vertices is asymptotically normal with mean $(8/27)n$ and variance $(152/729)n$. We also show that the distribution of the number of 3-connected components in a random 2-connected triangulation with $n+2$ vertices is asymptotically normal with mean $n/3$ and variance $\frac{8}{ 27}n$ . 
@article{DMTCS_2010_special_258_a33,
     author = {Gao, Zhicheng and Schaeffer, Gilles},
     title = {The distribution of the number of small cuts in a random planar triangulation},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2010},
     volume = {DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)},
     doi = {10.46298/dmtcs.2797},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2797/}
}
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%A Schaeffer, Gilles
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%J Discrete mathematics & theoretical computer science
%D 2010
%V DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)
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Gao, Zhicheng; Schaeffer, Gilles. The distribution of the number of small cuts in a random planar triangulation. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010). doi: 10.46298/dmtcs.2797

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