On 17.12.2009 at 12:20 in corridor, there is the following noon lecture:
Fractional total colorings of graphs of high girth
(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.
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