Cut vertices in random planar maps (Q6199192)

Summary: 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.