Triangle-factors in powers of graphs

In this paper, we investigate existence of triangle-factors, that is 2-factors in which every cycle is of length 3, in powers of graphs of order 3k,k ≥ 1. It is easy to show that G4 contains a triangle-factor for any connected graph and G3 contains a triangle-factor for any connected claw-free graph G Our main result is that G3 contains a triangle-factor for any 2-connected graph G. We also show, using the same method, that any 2-connected claw-free graph contains a P3-factor which implies that the square of the graph contains a triangle-factor.