Geodesic
On the Vertex Separation of Cactus Graphs
Serdica Journal of Computing, Tome 1 (2007) no. 1, pp. 45-72.

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This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a main theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.
Keywords: Algorithmic Graph Theory, Computational Complexity, Vertex Separation, Linear Layout, Layout Extensibility, Layout Stretchability, Cactus Graph 
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Markov, Minko. On the Vertex Separation of Cactus Graphs. Serdica Journal of Computing, Tome 1 (2007) no. 1, pp. 45-72. http://geodesic.mathdoc.fr/item/SJC_2007_1_1_a5/