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

Date and Time: Tuesday, September 22, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Abhigyan Ghosh

Extremal Graphs for Ramsey-Turán Numbers

For integers r and t and a function f(n) define the r-Ramsey-Turán number RT_r( n, K_t, f(n) ) to be the maximum number of edges in an n-vertex K_t-free graph G, such that α_r(G) ≤ f(n). Here α_r(G) denotes the maximum number of vertices in an K_r-free induced subgraph of G. Erdős, Hajnal, Simonovits, Sós, and Szemerédi conjectured the structure of the extremal graphs for RT_r( n, K_t, o(n) ); Balogh and Lenz provided a construction showing lower bounds for t≤2r. In my thesis I expanded upon the construction of Balogh and Lenz to show new extremal structures. These constructions show improved lower bounds which refute the long-standing conjecture of Erdős et al.

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