Cut Vertices in Random Planar Maps

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.