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 A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, March 27, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Anita Liebenau (University of Warwick)

What is Ramsey-equivalent to the clique?

A graph G is Ramsey for H if every two-colouring of the edges of G contains a monochromatic copy of H. Two graphs H and H' are Ramsey-equivalent if every graph G is Ramsey for H if and only if it is Ramsey for H'. We study the problem of determining which graphs are Ramsey-equivalent to the complete graph Kk. A famous theorem of Folkman implies that any graph H which is Ramsey-equivalent to Kk must contain Kk.

In this talk, we show that the only connected graph which is Ramsey-equivalent to Kk is itself. This gives a negative answer to the question of Szabó, Zumstein, and Zürcher on whether Kk is Ramsey-equivalent to Kk.K2, the graph on k+1 vertices consisting of Kk with a pendant edge. 

We also address the question of which non-connected graphs are Ramsey-equivalent to Kk. Let f(k,t) be the maximum f such that the graph H=Kk+fKt, consisting of Kk and f disjoint copies of Kt, is Ramsey-equivalent to Kk. Szabó, Zumstein, and Zürcher gave a lower bound on f(k,t). We prove an upper bound on f(k,t) which is roughly within a factor 2 of the lower bound. 

Joint work with J. Fox, A. Grinshpun, Y. Person and T. Szabó.


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