Leafy spanning trees in hypercubes

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Abstract

We prove that the d-dimensional hypercube, Qd, with n = 2d vertices, contains a spanning tree with at least leaves. This improves upon the bound implied by a more general result on spanning trees in graphs with minimum degree δ, which gives (1 - O(log log n)/log2n)n as a lower bound on the maximum number of leaves in spanning trees of n-vertex hypercubes. © 2001 Elsevier Science Ltd. All rights reserved.

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Duckworth, W., Dunne, P. E., Gibbons, A. M., & Zito, M. (2001). Leafy spanning trees in hypercubes. Applied Mathematics Letters, 14(7), 801–804. https://doi.org/10.1016/S0893-9659(01)00047-7

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