Abstract.
The decycling number, ∇(G), of a graph G is the least number of vertices of G whose deletion results in an induced subgraph without any cycles. Improved bounds are obtained for the decycling number ∇(Q n ) of the hypercube Q n . Further, it is shown that ∇(Q n )=2n −1−A(n,4) if and only if Q n has a minimum decycling set that consists of pairwise non-adjacent vertices, where A(n,4) denotes the size of a maximum binary code of length n and minimum Hamming distance 4.
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Research supported by NSERC
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Pike, D. Decycling Hypercubes. Graphs and Combinatorics 19, 547–550 (2003). https://doi.org/10.1007/s00373-003-0529-9
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DOI: https://doi.org/10.1007/s00373-003-0529-9