  A triangulation of a polygon is a subdivision of it into triangles, using
diagonals between its vertices. Two different triangulations of a polygon can
be related by a sequence of flips: a flip replaces a diagonal by the unique
other diagonal in the quadrilateral it defines. In this paper, we study
coloured triangulations and coloured flips. In this more general situation, it
is no longer true that any two triangulations can be linked by a sequence of
(coloured) flips. In this paper, we study the connected components of the
coloured flip graphs of triangulations. The motivation for this is a result of
Gravier and Payan proving that the Four-Colour Theorem is equivalent to the
connectedness of the flip graph of 2-coloured triangulations.
