In this paper, we study the k-tree partition problem which is a partition of the set of edges of a graph into k edge-disjoint 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 (n - 2) × (n - 2) area planar straight line drawing of maximal planar graphs using Schnyder's realizers [15], which are a 3-tree partition of the inner edges. Maximal planar bipartite graphs have a 2-tree 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 NP-hardness of the k-tree partition problem for general graphs and k > 2. This parallels NP-hard partition problems for the vertices [3], but it contrasts the efficient computation of partitions into forests (also known as arboricity) by matroid techniques [7]. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Biedl, T., & Brandenburg, F. J. (2007). Partitions of graphs into trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4372 LNCS, pp. 430–439). Springer Verlag. https://doi.org/10.1007/978-3-540-70904-6_41
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