Counting disjoint hypercubes in Fibonacci cubes

We provide explicit formulas for the maximum number q(k)(n) of disjoint subgraphs isomorphic to the k-dimensional hypercube in the n-dimensional Fibonacci cube Gamma(n), for small k, and prove that the limit of the ratio of such cubes to the number of vertices in Gamma(n), is 1/2(k) for arbitrary k. This settles a conjecture of Gravier, Mollard, Spacapan and Zemljic about file limiting behavior of q(k)(n). (C) 2016 Elsevier B.V. All rights reserved.