Planar graphs without 4-, 7-, 9-cycles and 5-cycles normally adjacent to 3-cycles.

A graph is (I , F) - partitionable if its vertex set can be partitioned into two parts such that one part I is an independent set, and the other F induces a forest. A graph is k - degenerate if every subgraph H contains a vertex of degree at most k in H. Bernshteyn and Lee defined a generalization of k -degenerate graphs, which is called weakly k -degenerate. In this paper, we show that planar graphs without 4-, 7-, 9-cycles, and 5-cycles normally adjacent to 3-cycles are both (I , F) -partitionable and weakly 2-degenerate. [ABSTRACT FROM AUTHOR]