On the uniform edge-partition of a tree

@article{Wu2007OnTU,
  title={On the uniform edge-partition of a tree},
  author={Bang Ye Wu and Hung-Lung Wang and Shih Ta Kuan and Kun-Mao Chao},
  journal={Discrete Applied Mathematics},
  year={2007},
  volume={155},
  pages={1213-1223}
}
We study the problem of uniformly partitioning the edge set of a tree with n edges into k connected components, where k ≤ n. The objective is to minimize the ratio of the maximum to the minimum number of edges of the subgraphs in the partition. We show that, for any tree and k ≤ 4, there exists a k-split with ratio at most two. For general k, we propose a simple algorithm that finds a k-split with ratio at most three in O(n log k) time. Experimental results on random trees are also shown. 

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