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

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, May 04, 2004, 12:15 pm

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

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

**Speaker**: Andreas Weissl

## On the number of labelled planar graphs with *n* nodes and *qn* edges

Recently C. McDiarmid, A. Steger and C. J.A. Welsh presented in
their paper "Random Planar Graphs", that there exists a constant
*gamma*_{l}, the 'labelled planar graph growth constant' such that
*(l(n) / n!)*^{{1/n}} converges to *gamma*_{l} as *n* approaches infinity, where *l(n)*
denotes the number of labelled planar graphs on *n* nodes. From this, they
deduced structural statements about the random planar graph.
My talk will focus on the number of planar graphs on *n*
nodes with a fixed number of edges, i.e. *f(n, qn)*. I will present
a proof sketch that *(f(n, qn) / n!)*^{{1/n}} converges to *gamma* as *n* goes to infinity.

(Joint work with C. McDiarmid, S. Gerke, A. Steger)

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