This is a post-peer-review, pre-copyedit version of an article published in European Journal of Combinatorics. The final authenticated version is available online at: https://doi.org/10.1016/j.ejc.2015.08.001

In this paper, we show that for every graph of maximum average degree bounded away from d and any two (d + 1)-colorings of it, one can transform one coloring into the other one within a polynomial number of vertex recolorings so that, at each step, the current coloring is proper. In particular, it implies that we can transform any 8-coloring of a planar graph into any other 8-coloring with a polynomial number of recolorings. These results give some evidence on a conjecture of Cereceda et al [8] which asserts that any (d + 2) coloring of a d-degenerate graph can be transformed into any other one using a polynomial number of recolorings. We also show that any (2d + 2)-coloring of a d-degenerate graph can be transformed into any other one with a linear number of recolorings.