A proper vertex coloring of a simple graph is -forested if the subgraph induced by the vertices of any two color classes is a -forest, i.e. a forest with maximum degree at most . The -forested coloring is also known as linear coloring, which has been extensively studied in the literature. In this paper, we aim to extend the study of -forested coloring to general -forested colorings for every by combinatorial means. Precisely, we prove that for a fixed integer and a planar graph with maximum degree and girth , if , then the -forested chromatic number of is actually . Moreover, we also prove that the -forested chromatic number of a planar graph with maximum degree and girth is provided . In addition, we show that the -forested chromatic number of an outerplanar graph is at most for every . In fact, all these results are proved for not only planar graphs but also for sparse graphs, i.e. graphs having a low maximum average degree , and we actually prove a choosability version of these results.