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

Date and Time: Tuesday, April 07, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Dániel Korándi (University of Oxford)

Exact stability for Turán's theorem

Turán's theorem says that an extremal K_r+1-free graph is r-partite. The Stability Theorem of Erdős and Simonovits shows that if a K_r+1-free graph with n vertices has close to the maximal t_r(n) edges, then it is close to being r-partite. In this talk we determine exactly the K_r+1-free graphs with at least m edges that are farthest from being r-partite, for any m > t_r(n) - δn². This extends work by Erdős, Győri and Simonovits, and proves a conjecture of Balogh, Clemen, Lavrov, Lidický and Pfender. Joint work with Alexander Roberts and Alex Scott.

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