Abstract
An ( F , F d ) -partition of a graph G is a partition of V ( G ) into sets V 1 and V 2 such that the induced graph G [ V 1 ] is a forest and G [ V 2 ] is a forest of maximum degree at most d . It was known that every planar graph without triangles is ( F , F 3 ) -partitionable. In this paper, we show that planar graphs without triangles and chordal 6-cycles are ( F , F 2 ) -partitionable.
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