Geodesic
Note on partitions of planar graphs
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 211-215

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Chartrand and Kronk in 1969 showed that there are planar graphs whose vertices cannot be partitioned into two parts inducing acyclic subgraphs. In this note we show that the same is true even in the case when one of the partition classes is required to be triangle-free only.
Keywords: planar graph, hereditary property of graphs, forest and triangle-free graph 
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Broere, Izak; Wilson, Bonita; Bucko, Jozef. Note on partitions of planar graphs. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 211-215. http://geodesic.mathdoc.fr/item/DMGT_2005_25_1-2_a19/