Total choosability of planar graphs with maximum degree 4

Let image be a planar graph with maximum degree image. It is known that image is image-totally choosable. It has been recently proved that if image has girth image, then image is image-totally choosable. In this note we improve the first result by showing that image is image-totally choosable and complete the latter one by showing that image is image-totally choosable if image has girth at least image.