Geodesic
Cut vertices in random planar maps
The electronic journal of combinatorics, Tome 30 (2023) no. 3

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Zbl DOI arXiv
The main goal of this paper is to determine the asymptotic behavior of the number $X_n$ of cut-vertices in random planar maps with $n$ edges. It is shown that $X_n/n \to c$ in probability (for some explicit $c>0$). For so-called subcritical classes of planar maps (like outerplanar maps) we obtain a central limit theorem, too. Interestingly the combinatorics behind this seemingly simple problem is quite involved.
DOI : 10.37236/11163
Classification : 05C80, 05C10, 05D40, 60C05, 60F05
Mots-clés : subcritical classes of planar maps, central limit theorem 
Michael Drmota; Marc Noy; Benedikt Stufler. Cut vertices in random planar maps. The electronic journal of combinatorics, Tome 30 (2023) no. 3. doi: 10.37236/11163
@article{10_37236_11163,
     author = {Michael Drmota and Marc Noy and Benedikt Stufler},
     title = {Cut vertices in random planar maps},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
     number = {3},
     doi = {10.37236/11163},
     zbl = {1533.05247},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11163/}
}
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