Decomposing the vertex set of a hypercube into isomorphic subgraphs

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 $X$.

arXiv comment10 pages

References in corpus (1)

• Edge Decompositions of Hypercubes by Paths

Cited by in corpus (3)

• Almost partitioning the hypercube into copies of a graph
• Tiling with punctured intervals
• Packing the Boolean lattice with copies of a poset