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

Date and Time: Tuesday, May 03, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Jozef Skokan (Univ. of Illinois at Urbana-Champaign and Univ. de São Paulo)

On a theorem of Luczak

For graphs L₁,..., L_k, the Ramsey number R(L₁, . . . , L_k) is the minimum integer N such that, in any coloring of the edges of the complete graph on N vertices by k colors, there exists a color i for which the corresponding color class contains L_i as a subgraph. Let C_n denote the cycle of length n. In 1973, Bondy and Erdős conjectured that if n is odd, then R(C_n,C_n,C_n) =4n-3. A great deal later, in 1999, a breakthrough was finally achieved by Luczak: he proved that R(C_n,C_n,C_n) = (4+o(1))n, where o(1) tends to 0 as n tends to infinity. In this talk, we shall outline a proof of the conjecture for all large enough n. This proof is heavily inspired on Luczak's proof, but gives the sharper result by exploiting certain stability results for extremal colourings.

Some recent related developments due to other authors will be discussed.

Joint work with M. Simonovits (Budapest) and Y. Kohayakawa (São Paulo).

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