Acyclic 6-choosability of Planar Graphs without 5-cycles and Adjacent 4-cycles

A proper vertex coloring of a graph is acyclic if every cycle uses at least three colors. A graph G is acyclically k-choosable if for any list assignment L = {L(v): v is an element of V(G)} with divide L(v) divide >= k for all v is an element of V(G), there exists a proper acyclic vertex coloring phi of G such that phi(v) is an element of L(v) for all v is an element of V(G). In this paper, we prove that if G is a planar graph and contains no 5-cycles and no adjacent 4-cycles, then G is acyclically 6-choosable.