Counting disjoint hypercubes in Fibonacci cubes

We provide explicit formulas for the maximum number qk(n) of disjoint subgraphs isomorphic to the k-dimensional hypercube in the n-dimensional Fibonacci cube Γn for small k, and prove that the limit of the ratio of such cubes to the number of vertices in Γn is 12k for arbitrary k. This settles a con...

Full description

Saved in:
Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 215; pp. 231 - 237
Main Authors Saygı, Elif, Eğecioğlu, Ömer
Format Journal Article
LanguageEnglish
Published Elsevier B.V 31.12.2016
Subjects
Fibonacci cube
Fibonacci number
Hypercube
Fibonacci cube
Fibonacci number
Hypercube
Online AccessGet full text
ISSN0166-218X
1872-6771
DOI10.1016/j.dam.2016.07.004

Cover

More Information
Summary:We provide explicit formulas for the maximum number qk(n) of disjoint subgraphs isomorphic to the k-dimensional hypercube in the n-dimensional Fibonacci cube Γn for small k, and prove that the limit of the ratio of such cubes to the number of vertices in Γn is 12k for arbitrary k. This settles a conjecture of Gravier, Mollard, Špacapan and Zemljič about the limiting behavior of qk(n).
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2016.07.004