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Feedback vertex set in hypercubes. (English) Zbl 1338.68218
Summary: Given a graph \(G= (V, E)\), the minimum feedback vertex set \(\overline{V}\) is a subset of vertices of minimum size whose removal induces an acyclic subgraph \(G'= (V \backslash\overline{V}, E')\). The problem of finding \(\overline{V}\) is \(\operatorname{NP}\)-hard for general networks but interesting polynomial solutions have been found for particular graph classes. In this paper we find close upper and lower bounds to the size of \(\overline{V}\) in a \(k\)-dimensional hypercube.

MSC:
68R10 Graph theory (including graph drawing) in computer science
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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