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

Cores of Vertex Transitive Graphs