On Disjoint hypercubes in Fibonacci cubes
Résumé
The {\em Fibonacci cube} of dimension $n$, denoted as $\Gamma_n$, is the subgraph of $n$-cube $Q_n$ induced by vertices with no consecutive 1's. We study the maximum number of disjoint subgraphs in $\Gamma_n$ isomorphic to $Q_k$, and denote this number by $q_k(n)$. We prove several recursive results for $q_k(n)$, in particular we prove that
$q_{k}(n) = q_{k-1}(n-2) + q_{k}(n-3)$. We also prove a closed formula in which $q_k(n)$ is given in terms of Fibonacci numbers, and finally we give the generating function for the sequence $\{q_{k}(n)\}_{n=0}^{ \infty}$.
Domaines
Combinatoire [math.CO]Origine | Fichiers produits par l'(les) auteur(s) |
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