# Prof. dr. Michael Drmota: The maximum degree of planar graphs

Date: 7. 12. 2012

Source: Mathematics colloquium

Source: Mathematics colloquium

Četrtek, 13. 12. 2012, ob 18:15 v predavalnici 2.02 na Jadranski 21.

**Michael Drmota**

Technische Universität Wien

McDiarmid and Reed showed in 2008 that the maximum degree Δ _{n} of a random labeled planar graph with *n* vertices satisfies with high probability *c*_{1 }log *n* < Δ _{n} < *c*_{2 }log *n* for suitable constants 0 < *c*_{1} < *c*_{2}. The purpose of this talk is to make this statement more accurate by showing that the precise limiting behavior of Δ _{n} is (with high probability) > ∣Δ _{n} − *c *log *n*∣ = *O*(log log *n*) for a constant *c* ≈ 2. 52946 that can be determined explicitly. The proof combines tools from analytic combinatorics and Boltzmann sampling techniques.