Drmota, M., Noy, M., & Stufler, B. (2023). Cut Vertices in Random Planar Maps. Electronic Journal of Combinatorics, 30(3), Article P3.32. https://doi.org/10.37236/11163
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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Journal:
Electronic Journal of Combinatorics
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ISSN:
1077-8926
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Date (published):
22-Sep-2023
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Number of Pages:
32
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Publisher:
ELECTRONIC JOURNAL OF COMBINATORICS
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Peer reviewed:
Yes
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Keywords:
Planar Maps; cut vertices
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Abstract:
The main goal of this paper is to determine the asymptotic behavior of the number Xn of cut-vertices in random planar maps with n edges. It is shown that Xn /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. Inter-estingly the combinatorics behind this seemingly simple problem is quite involved.
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Research Areas:
Mathematical and Algorithmic Foundations: 95% Computer Science Foundations: 5%
