  A core of a graph X is a vertex minimal subgraph to which X admits a
homomorphism. Hahn and Tardif have shown that for vertex transitive graphs, the
size of the core must divide the size of the graph. This motivates the
following question: when can the vertex set of a vertex transitive graph be
partitioned into sets each of which induce a copy of its core? We show that
normal Cayley graphs and vertex transitive graphs with cores half their size
always admit such partitions. We also show that the vertex sets of vertex
transitive graphs with cores less than half their size do not, in general, have
such partitions.

Combinatorics