Every Graph Embedded on the Surface with Euler Characteristic Number ε = −1 is Acyclically 11-choosable

A proper vertex coloring of a graph G is acyclic if there is no bicolored cycles in G . A graph G is acyclically k-choosable if for any list assignment L = { L ( v ): v ∈ V ( G )} with ∣ L ( v )∣ ≥ k for each vertex v ∈ V ( G ), there exists an acyclic proper vertex coloring ϕ of G such that ϕ ( v ) ∈ L ( v ) for each vertex v ∈ V ( G ). In this paper, we prove that every graph G embedded on the surface with Euler characteristic number ε = −1 is acyclically 11-choosable.