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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, October 30, 2014, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Stoyan Dimitrov (University of Sofia)

Vertex Folkman number is defined as $F_{v}(a_{1}, a_{2},..,a_{r};q)= \min\{ |V(G)| : G\xrightarrow{v} (a_{1}, a_{2},..,a_{r})$ and $\omega (G) < q\}$. Here $G\xrightarrow{v} (a_{1}, a_{2},...,a_{r})$ means that in every $r$ - coloring of the vertices of G, for some color $i\in\{1,2, \ldots ,r\}$, there exists a monochromatic clique $K_{a_{i}}$. In the case of $a_{1} = a_{2} = \ldots = a_{r} = 2$, we write $F(2_{r};q)$. This case is of special importance, because $G\xrightarrow{v} (a_{1}, a_{2},...,a_{r})$ is equivalent to $\chi (G) > r$. Only one among the numbers $F(2_{r};q)$, $q\geq r-1$ and only three among the numbers $F(2_{r};r-2)$ are still not known. The focus of this work is on one of them, namely $F(2_{7};5)$.

It is previously known that $F(2_{7};5)>15$ (*Nenov*, 2009) and $F(2_{7};5)\leq 47$ (follows easily from a graph construction method by *Mycielski*, 1955). In this talk we explain how the new lower bound $F(2_{7};5)>17$ was obtained with the help of computer - assisted graph generation methods. Moreover, we present a simple proof of the upper bound $F(2_{7};5)\leq 22 $.

Joint work with Nedyalko Nenov

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