Star Coloring and Acyclic Coloring of Locally Planar Graphs
Ken‐ichi Kawarabayashi, Bojan Mohar · SIAM Journal on Discrete Mathematics · 2010
It is proved that every graph embedded in a fixed surface with sufficiently large edge-width is acyclically 7-colorable and that its star chromatic number is at most $2s_0^*+3$, where $s_0^*\leq20$ is the maximum star chromatic number for the class of all planar graphs.