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Pré-Publication, Document De Travail Année : 2010

On Vertex Partitions of Hypercubes by Isometric Trees

Michel Mollard

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 $n'\geq n$
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Dates et versions

hal-00535683 , version 1 (12-11-2010)
hal-00535683 , version 2 (14-03-2011)

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  • HAL Id : hal-00535683 , version 1

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Michel Mollard. On Vertex Partitions of Hypercubes by Isometric Trees. 2010. ⟨hal-00535683v1⟩
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