# Noon lecture

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On 17.12.2009 at 12:20 in corridor, there is the following noon lecture:

# Fractional total colorings of graphs of high girth

## František Kardoš

## Abstract

(joint work with Daniel Kral, Jean-Sebastien Sereni)

Reed conjectured that for every $\varepsilon > 0$ and every integer $\Delta$ there exists $g$ such that the fractional total chromatic number of every graph $G$ of maximum degree $\Delta$ and girth at least $g$ is at most $\Delta+1+\varepsilon$. The conjecture was proven to be true in a stronger form when $\Delta$ is three or an even integer by Kral, Kaiser and King. We settle the conjecture by proving that it holds also for the remaining cases, i.e. when $\Delta$ is an odd integer.

list of noon lectures ( 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | future lectures)

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