ArticleOriginal scientific text
Title
Note on partitions of planar graphs
Authors 1, 1, 2
Affiliations
- Rand Afrikaans University, Johannesburg, Republic of South Africa
- Department of Applied Mathematics, Faculty of Economics, Technical University, B. Nĕmcovej, 040 01 Košice, Slovak Republic
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
Bibliography
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Pages:
211-215
Main language of publication
English
Received
2003-12-05
Accepted
2004-11-03
Published
2005
DOI: 10.7151/dmgt.1273
Exact and natural sciences