Planar graphs without 4-cycles adjacent to 3-cycles are list vertex 2-arborable. (English summary) J. Graph Theory 62 (2009), no. 3, 234–240. Summary: “It is known that not all planar graphs are 4-choosable; neither all of them are vertex 2-arborable. However, planar graphs without 4-cycles and even those without 4-cycles adjacent to 3-cycles are known to be 4-choosable. We extend this last result in terms of covering the vertices of a graph by induced subgraphs of variable degeneracy. In particular, we prove that every planar graph without 4-cycles adjacent to 3-cycles can be covered by two induced forests.