Decomposing a triangle-free planar graph into a forest and a subcubic forest

We strengthen a result of Dross et al. (2017) that the vertex set of every triangle-free planar graph can be decomposed into a set that induces a forest and a set that induces a forest with maximum degree at most 5, showing that 5 can be replaced by 3. (c) 2023 Elsevier Ltd. All rights reserved.