Note on partitions of planar graphs
Izak Broere, Bonita S. Wilson, Jozef Bucko (2005)
Discussiones Mathematicae Graph Theory
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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.