Decomposing the vertex set of a hypercube into isomorphic subgraphs [article]

Vytautas Gruslys
2016 arXiv   pre-print
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:1611.02021v1 fatcat:prcn5wvm5jhmrhnarn7o3jm3sa