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- W2946859941 abstract "Let L(G) denote the maximum number of leaves in any spanning tree of a connected graph G. We show the (known) result that for the n-cube Qn, L(Qn) ∼ 2n = |V(Qn)| as n → ∞. Examining this more carefully, consider the minimum size of a connected dominating set of vertices γc(Qn), which is 2n − L(Qn) for n ≥ 2. We show that γc(Qn) ∼ 2n/n, which rather surprisingly is no larger than the asymptotic behavior of the domination number γ(Qn). We use Hamming codes and an “expansion” method to construct leafy spanning trees in Qn." @default.
- W2946859941 created "2019-06-07" @default.
- W2946859941 creator A5011011757 @default.
- W2946859941 date "2022-04-19" @default.
- W2946859941 modified "2023-09-25" @default.
- W2946859941 title "Spanning trees and domination in hypercubes" @default.
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- W2946859941 doi "https://doi.org/10.1515/9783110754216-013" @default.
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