Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, December 03, 2009, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Reto Spöhel

Upper bounds for asymmetric Ramsey properties of random graphs

Consider the following problem: Is there a coloring of the edges of the random graph $G_{n,p}$ with two colors such that there is no monochromatic copy of some fixed graph $F$? A celebrated result by Rdl and Rucinski (1995) states a general threshold function $p_0(F,n)$ for the existence of such a coloring. Kohayakawa and Kreuter (1997) conjectured a general threshold function for the asymmetric case (where different graphs $F_1$ and $F_2$ are forbidden in the two colors), and verified this conjecture for the case where both graphs are cycles.

Implicit in their work is the following more general statement: The conjectured threshold function is an upper bound on the actual threshold provided that i) the two graphs satisfy some balancedness condition, and ii) the so-called K{\L}R-Conjecture is true for the sparser of the two graphs. We present a new upper bound proof that does not depend on the K{\L}R-Conjecture. Together with earlier lower bound results [Marciniszyn, Skokan, S., Steger (2006)], this yields in particular a full proof of the Kohayakawa-Kreuter conjecture for the case where both graphs are cliques.

Joint work with Yoshiharu Kohayakawa and Mathias Schacht.

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

Previous talks by year:   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