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

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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