Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information|
Date and Time: Tuesday, September 22, 2020, 12:15 pm
Duration: 30 minutes
Location: Zoom: conference room
Speaker: Abhigyan Ghosh
For integers r and t and a function f(n) define the r-Ramsey-Turán number RTr( n, Kt, f(n) ) to be the maximum number of edges in an n-vertex Kt-free graph G, such that αr(G) ≤ f(n). Here αr(G) denotes the maximum number of vertices in an Kr-free induced subgraph of G. Erdős, Hajnal, Simonovits, Sós, and Szemerédi conjectured the structure of the extremal graphs for RTr( n, Kt, 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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