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.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login