Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, November 28, 2013, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Frank Mousset

Consider the problem of counting the K_{r+1}-free graphs of order n. It is well known (and an old result) that the number of such graphs is 2^{(1-1/r)n^2/2 + o(n^2)}. However, if r tends to infinity with n, then this is not a satisfactory answer. Very recently, it has been become possible to prove an analogous result that covers a large range of values for r: if r = o((log n)^{1/5}), then there are 2^{(1-1/r)n^2/2 + o(n^2/r)} K_{r+1}-free graphs of order n. The proof is based on the recent hypergraph container theorems of Saxton/Thomason and Balogh/Morris/Samotij, in combination with a theorem of Lovász and Simonovits.

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