Planar graphs are 1-relaxed, 4-choosable

We show that every planar graph G=(V,E) is 1-relaxed, 4-choosable. This means that, for every list assignment L that assigns a set of at least four colors to each vertex, there exists a coloring f such that f(v)@?L(v) for every vertex v@?V and each color class f^-^1(@a) of f induces a subgraph with maximum degree at most 1.