Abstract
We prove that the game chromatic and the game colouring number of the class of orientations of cactuses with girth of 2 or 3 is 4. We improve this bound for the class of orientations of certain forest-like cactuses to the value of 3. These results generalise theorems on the game colouring number of undirected forests (Faigle et al., 1993 [3]) resp. orientations of forests (Andres, 2009 [1]). For certain undirected cactuses with girth 4 we also obtain the tight bound 4, thus improving a result of Sidorowicz (2007) [8].
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