Cut Vertices in Random Planar Maps

2021/04/29 by Michael Drmota, Drmota, Michael, Marc Noy +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.CO #math.PR

paper · pdf · doi:10.48550/arxiv.2104.14151

arxiv created 2021/04/29 · openalex publication_date 2021/04/29 · arxiv updated 2021/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 → 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.

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