DMGT

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
Johannesburg, Republic of South Africa
e-mail: ib@rau.ac.za

Jozef Bucko

Department of Applied Mathematics
Faculty of Economics, Technical University
B. Nemcovej, 040 01 Košice, Slovak Republic
e-mail: bucko@tuke.sk

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