  The reconfiguration graph $R_k(G)$ for the $k$-colorings of a graph $G$ has
as vertex set the set of all possible proper $k$-colorings of $G$ and two
colorings are adjacent if they differ in the color of exactly one vertex. A
result of Bousquet and Perarnau (2016) regarding graphs of bounded degeneracy
implies that if $G$ is a planar graph with $n$ vertices, then $R_{12}(G)$ has
diameter at most $6n$. We improve on the number of colors, showing that
$R_{10}(G)$ has diameter at most $8n$ for every planar graph $G$ with $n$
vertices.
