Every toroidal graph is acyclically 8-choosable

A proper coloring of a graph G is acyclic if G contains no 2-colored cycle. A graph G is acyclically L-list colorable if for a given list assignment L = {L(v): v . V (G)}, there exists a proper acyclic coloring . of G such that .(v) . L(v) for all v . V (G). If G is acyclically L-list colorable for any list assignment L with |L(v)| . k for all v . V (G), then G is acyclically k-choosable. In this article, we prove that every toroidal graph is acyclically 8-choosable.