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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, April 27, 2010, 12:15 pm

**Duration**: This information is not available in the database

**Location**: OAT S15/S16/S17

**Speaker**: Torsten Mütze

One of the fundamental topics in Ramsey theory is to study, for a forbidden graph F, the family of all graphs G with the property that any two-coloring of the edges of G contains a monochromatic copy of F (we say that such a graph G is F-Ramsey). The classical Ramsey number R(F) for instance is defined as the minimum number of vertices among all graphs G that are F-Ramsey (e.g., R(K_3)=6, as any graph on less than 6 vertices can be two-colored without a monochromatic triangle, and any two-coloring of the edges of K_6 contains a monochromatic triangle). Beside the minimum number of vertices among all F-Ramsey graphs, also the minimum number of edges, and the minimum clique-number among these graphs have been studied intensively. In this talk, we discuss results from [1] and [2] concerning the following question of this flavor: What is the minimum density among all graphs G that are F-Ramsey, where the density of a graph G is defined as m(G):=max_{H\subseteq G} e(H)/v(H) (the maximum is over all subgraphs H of G)? One of the results is, that the sparsest graph that is K_n-Ramsey is the complete graph on R(K_n) vertices.

Talk mainly based on

[1] A. Kurek and A. Rucinski, Globally sparse vertex-Ramsey graphs, J. Graph Theory 18 (1) (1994) 73--81.

[2] A. Kurek and A. Rucinski. Two variants of the size Ramsey number, Discuss. Math. Graph Th. 25 (2005) 141--149.

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