Abstract
All graphs have cycle separators. (A single vertex is regarded as a trivial cycle.) In sequential computation, a cycle separator can be found in O(n + e) time for any undirected graph of n vertices and e edges; in O((n + e) log n) time for any directed graph. In parallel computation, it is in deterministic NC to convert any depth-first search forest of any graph into a cycle separator. Moreover, finding a cycle separator for any planar directed graph is in deterministic NC; consequently, finding a depth-first search forest in any planar directed graph is in deterministic NC, too.
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supported in part by a 1987 Summer Faculty Fellowship from Indiana University at Bloomington.
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References
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© 1988 Springer-Verlag Berlin Heidelberg
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Kao, MY. (1988). All graphs have cycle separators and planar directed depth-first search is in DNC. In: Reif, J.H. (eds) VLSI Algorithms and Architectures. AWOC 1988. Lecture Notes in Computer Science, vol 319. Springer, New York, NY. https://doi.org/10.1007/BFb0040373
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DOI: https://doi.org/10.1007/BFb0040373
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