  Two (proper) colorings of a graph are adjacent if they differ on exactly one
vertex. Jerrum proved that any $(d + 2)$-coloring of any d-degenerate graph can
be transformed into any other via a sequence of adjacent colorings. A result of
Bonamy et al. ensures that a shortest transformation can have a quadratic
length even for $d = 1$. Bousquet and Perarnau proved that a linear
transformation exists for between $(2d + 2)$-colorings. It is open to determine
if this bound can be reduced. In this note, we prove that it can be reduced for
graphs of treewidth 2, which are 2-degenerate. There exists a linear
transformation between 5-colorings. It completes the picture for graphs of
treewidth 2 since there exist graphs of treewidth 2 such a linear
transformation between 4-colorings does not exist.
