# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, December 14, 2004, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Mihyun Kang (HU Berlin)

## The Asymptotic Number of Outerplanar Graphs

An outerplanar graph is a graph that can be embedded in the plane in
such a way that every vertex lies on the outer face. We decompose
outerplanar graphs along their connectivity structure and derive the
equations of the exponential generating functions. With a singularity
analysis of these equations we show that the number of labeled
outerplanar graphs on *n* vertices is asymptotically *C
n*^{-5/2}γ^{n}n! for constants *C, γ = 7.32098*. We also
show that for constants *α*, *β*, the probability of a random
outerplanar graph chosen uniformly at random being connected is
asymptotically *e*^{-α} = 0.86166, and that the expected
number of edges in a random outerplanar graph on *n* vertices is
asymptotically *β n = 1.56251n*.

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