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

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

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Frank Mousset

Counting graphs without large cliques

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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