Partitions of Graphs into TreesBiedl, Therese and Brandenburg, Franz J. (2007) Partitions of Graphs into Trees. In: Graph Drawing 14th International Symposium, GD 2006, September 1820, 2006 , pp. 430439(Official URL: http://dx.doi.org/10.1007/9783540709046_41). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783540709046_41
AbstractIn this paper, we study the ktree partition problem which is a partition of the set of edges of a graph into k edgedisjoint trees. This problem occurs at several places with applications e.g. in network reliability and graph theory. In graph drawing there is the still unbeaten (n2) x (n2) area planar straight line drawing of maximal planar graphs using Schnyder's realizers [15]}, which are a 3tree partition of the inner edges. Maximal planar bipartite graphs have a 2tree partition, as shown by Ringel [14]. Here we give a different proof of this result with a linear time algorithm. The algorithm makes use of a new ordering which is of interest of its own. Then we establish the NPhardness of the ktree partition problem for general graphs and k >= 2. This parallels NPhard partition problems for the vertices [3], but it contrasts the efficient computation of partitions into forests (also known as arboricity) by matroid techniques [7].
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