Comment on: “Centers of quasi-homogeneous polynomial planar systems” [Nonlinear Anal. RWA 13 (2012) 419]

We describe a counter-example which shows that (2) of theorem (11) in Algaba et al. (2012) is not correct. This part of the theorem, pinpoints whether the origin of quasi-homogeneous system (15) in Algaba et al. (2012) is a center or not. It is shown in this note that the given necessary and sufficient conditions of theorem (11), in Algaba et al. (2012) are not complete.