A local algorithm is a distributed algorithm that completes after a constant
number of synchronous communication rounds. We present local approximation
algorithms for the minimum dominating set problem and the maximum matching
problem in 2-coloured and weakly 2-coloured graphs. In a weakly 2-coloured
graph, both problems admit a local algorithm with the approximation factor
$(\Delta+1)/2$, where $\Delta$ is the maximum degree of the graph. We also give
a matching lower bound proving that there is no local algorithm with a better
approximation factor for either of these problems.