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 -> 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.