  Solitaire {\sc Flood-it}, or {\sc Honey-Bee}, is a game played on a colored
graph. The player resides in a source vertex. Originally his territory is the
maximal connected, monochromatic subgraph that contains the source. A move
consists of calling a color. This conquers all the nodes of the graph that can
be reached by a monochromatic path of that color from the current territory of
the player. It is the aim of the player to add all vertices to his territory in
a minimal number of moves. We show that the minimal number of moves can be
computed in polynomial time when the game is played on AT-free graphs.
