  A $k$-frugal colouring of a graph $G$ is a proper colouring of the vertices
of $G$ such that no colour appears more than $k$ times in the neighbourhood of
a vertex. This type of colouring was introduced by Hind, Molloy and Reed in
1997. In this paper, we study the frugal chromatic number of planar graphs,
planar graphs with large girth, and outerplanar graphs, and relate this
parameter with several well-studied colourings, such as colouring of the
square, cyclic colouring, and $L(p,q)$-labelling. We also study frugal
edge-colourings of multigraphs.
