On partitioning a planar graph into two forests of maximum degree at most three

An [Formula: see text]-partition of a graph [Formula: see text] is a partition of [Formula: see text] into two subsets [Formula: see text] and [Formula: see text] such that the induced subgraph [Formula: see text] is a forest of maximum degree at most [Formula: see text] for [Formula: see text]. In 2021, Cho et al.[Formula: see text][Formula: see text]proved that every planar graph without [Formula: see text]- and [Formula: see text]-cycles has an [Formula: see text]-partition. In this paper, we prove that every planar graph without [Formula: see text]-, [Formula: see text]- and [Formula: see text]-cycles has an [Formula: see text]-partition for a fixed [Formula: see text].