Leafy spanning trees in hypercubes

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.