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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.)
##### Keywords:
feedback vertex set; cycle; hypercube; codes; combinatorial problems
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##### References:
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