  Graph partitioning, or the dividing of a graph into two or more parts based
on certain conditions, arises naturally throughout discrete mathematics, and
problems of this kind have been studied extensively. In the 1990s, Ando
conjectured that the vertices of every cubic graph can be partitioned into two
parts that induce isomorphic subgraphs. Using probabilistic methods together
with delicate recolouring arguments, we prove Ando's conjecture for large
connected graphs.
