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Discussiones Mathematicae Graph Theory 25(1-2) (2005)
211-215
DOI: https://doi.org/10.7151/dmgt.1273
NOTE ON PARTITIONS OF PLANAR GRAPHS
| Izak Broere and Bonita S. Wilson
Rand Afrikaans University |
Jozef Bucko
Department of Applied Mathematics |
Abstract
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.
2000 Mathematics Subject Classification: 05C15.
References
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Received 5 December 2003
Revised 3 November 2004
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