Monday February 26th at 4.30pm

As a corollary this implies that for cubic graphs of order $n$ and girth $g\geq 5$ the domination number $\gamma$ satisfies $\gamma \leq \left(\frac{44}{135}+\frac{82}{135g}\right)n$

which improves recent results due to Kostochka and Stodolsky (2005) and Kawarabayashi, Plummer and Saito (2006)

for large enough girth. Furthermore, it confirms a conjecture of Reed about cubic graphs which turned out to be false in general for graphs of girth at least 83.

(This is joint work with Christian Loewenstein.)