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General topological results on the construction of a minimum essential set of a directed graph

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1 Author(s)

In this paper we present general topological results on the construction of a minimum essential set or minimum feedback vertex set of a directed graph. The results include all the existing topological rules that identify subsets of a minimum essential set as special cases. Moreover, we show how a class of topological results can be systematically generated by using the theory of strongly adjacent polygons. We use the topological results to provide an algorithm which constructs a minimal essential set of an n -vertex symmetric directed graph, a maximal stable set of an n-vertex undirected graph and an essential set of an n -vertex arbitrary directed graph in \theta (n^2) computation steps and such that these solutions are within a known tolerance of the optimal value.

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Circuits and Systems, IEEE Transactions on  (Volume:27 ,  Issue: 4 )