在随机平面图中切割顶点

International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms Pub Date : 2021-04-29 DOI:10.4230/LIPIcs.AofA.2020.10

M. Drmota, M. Noy, Benedikt Stufler

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引用次数: 5

摘要

本文的主要目的是确定具有$n$条边的随机平面映射中切割顶点数目$X_n$的渐近行为。它显示了$X_n/n \到c$的概率(对于某些显式的$c> $)。对于所谓的次临界类的平面映射(如外平面映射)，我们也得到了一个中心极限定理。有趣的是，这个看似简单的问题背后的组合学是相当复杂的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Cut Vertices in Random Planar Maps

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.

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International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms

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