On Vertex Partitions of Hypercubes by Isometric Trees
Résumé
When $n=2^m-1$ M.Ramras proved, by a counting argument, that for any isometrically embedded tree $T$ on $n$ edges in $Q_n$ there exists a group of translations $G$ such that $\left\{g(T); g\in G \right\}$ is a vertex partition of $Q_n$. Considering a more general context we are able to give an explicit construction of $G$ and can construct non group vertex partitions by isometric trees. We extend also this problem to vertex partition of $Q_{n'}$ by translates of an isometrically embedded tree on $n=2^m-1$ edges for any $n'\geq n$
Domaines
Combinatoire [math.CO]Origine | Fichiers produits par l'(les) auteur(s) |
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