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<p><b>Abstract</b>—Let <tmath>$G$</tmath> be an undirected graph and <tmath>$T$</tmath> be a spanning tree of <tmath>$G$</tmath>. In this paper, an efficient parallel algorithm is proposed for determining whether <tmath>$T$</tmath> is an unordered depth-first search tree of <tmath>$G$</tmath>. The proposed algorithm runs in <tmath>$O(m/p + \log m)$</tmath> time using <tmath>$p$</tmath> processors on the EREW PRAM, where <tmath>$m$</tmath> is the number of edges contained in <tmath>$G$</tmath>. It is cost-optimal and achieves linear speedup.</p>
Depth-first search trees, spanning trees, parallel algorithms, PRAM, the Euler-tour technique.

B. Wang, C. Peng and J. Wang, "Recognizing Unordered Depth-First Search Trees of an Undirected Graph in Parallel," in IEEE Transactions on Parallel & Distributed Systems, vol. 11, no. , pp. 559-570, 2000.
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