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arXiv · 1611.02021

Decomposing the vertex set of a hypercube into isomorphic subgraphs

Vytautas Gruslys
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Abstract

Let $G$ be an induced subgraph of the hypercube $Q_k$ for some $k$. We show that if $|G|$ is a power of $2$ then, for sufficiciently large $n$, the vertex set of $Q_n$ can be partitioned into induced copies of $G$. This answers a question of Offner. In fact, we prove a stronger statement: if $X$ is a subset of $\{0,1\}^k$ for some $k$ and if $|X|$ is a power of $2$, then, for sufficiently large $n$, $\{0,1\}^n$ can be partitioned into isometric copies of $X$.

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Vytautas Gruslys. 2016-11-07. Decomposing the vertex set of a hypercube into isomorphic subgraphs. https://arxiv.org/abs/1611.02021

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