# Edge-disjoint spanning trees and depth-first search

@article{Tarjan2004EdgedisjointST, title={Edge-disjoint spanning trees and depth-first search}, author={Robert E. Tarjan}, journal={Acta Informatica}, year={2004}, volume={6}, pages={171-185} }

SummaryThis paper presents an algorithm for finding two edge-disjoint spanning trees rooted at a fixed vertex of a directed graph. The algorithm uses depthfirst search and an efficient method for computing disjoint set unions. It requires O (eα(e, n)) time and O(e) space to analyze a graph with n vertices and e edges, where α (e, n) is a very slowly growing function related to a functional inverse of Ackermann's function.

## 151 Citations

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- 2010

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This work presents an algorithm achieving similar bounds that can be easily adopted to the parallel environment and provides, in a seamless manner, nearly optimal (to poly log n factors) deterministic parallel algorithms for maintaining a DFS tree in the semi-streaming environment and a restricted distributed model.

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### Planar Reachability Under Single Vertex or Edge Failures

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### Near Optimal Parallel Algorithms for Dynamic DFS in Undirected Graphs

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This work presents an algorithm achieving similar bounds, that can be adopted easily to the parallel environment, and provides the first parallel, semi-streaming and distributed algorithms for maintaining a DFS tree in the dynamic setting.

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