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

Date: 7. 12. 2012
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 clog n < Δ n < clog n for suitable constants 0 < c1 < c2. 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 − 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.

http://wiki.fmf.uni-lj.si/wiki/MatematicniKolokviji