  Without further ado, we present the P_3-game. The P_3-game is decidable for
elementary classes of graphs such as paths and cycles. From an algorithmic
point of view, the connected P_3-game is fascinating. We show that the
connected P_3-game is polynomially decidable for classes such as trees, chordal
graphs, ladders, cacti, outerplanar graphs and circular arc graphs.
