Counting disjoint hypercubes in Fibonacci cubes


SAYGI E. , Eğecioğlu O.

DISCRETE APPLIED MATHEMATICS, cilt.215, ss.231-237, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 215
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.dam.2016.07.004
  • Dergi Adı: DISCRETE APPLIED MATHEMATICS
  • Sayfa Sayıları: ss.231-237

Özet

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.