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http://dx.doi.org/10.4134/JKMS.2005.42.4.847

ON TWO GRAPH PARTITIONING QUESTIONS  

Rho, Yoo-Mi (Department of Mathematics Incheon University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.4, 2005 , pp. 847-856 More about this Journal
Abstract
M. Junger, G. Reinelt, and W. R. Pulleyblank asked the following questions ([2]). (1) Is it true that every simple planar 2-edge connected bipartite graph has a 3-partition in which each component consists of the edge set of a simple path? (2) Does every simple planar 2-edge connected graph have a 3-partition in which every component consists of the edge set of simple paths and triangles? The purpose of this paper is to provide a positive answer to the second question for simple outerplanar 2-vertex connected graphs and a positive answer to the first question for simple planar 2-edge connected bipartite graphs one set of whose bipartition has at most 4 vertices.
Keywords
planar graphs; outerplanar graphs; 2-edge connected graphs; 2-vertex connected graphs; bipartite graphs; 3-partitions;
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  • Reference
1 B. Bollobas, Graph theory, Springer-Verlag, New York, 1979
2 M. Junger, G. Reinelt, and W. R. Pulleyblank, On partitioning the edges of graphs into connected subgraphs, J. Graph Theory 9 (1985), 539-549   DOI
3 Douglas B. West, Introduction to graph theory, Prentice-Hall, New Jersey, 1996